Question 2 :
Two dice are thrown. Find the odds in favour of getting the sum $4$.<br/>
Question 3 :
A die is thrown .The probability that the number comes up even is ______ .
Question 4 :
A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the number between 1 to 15. What is the probability that it will point to an odd number.
Question 5 :
The probability of an event happening and the probability of the same event not happening (or the complement) must be a <br/>
Question 7 :
A fair dice has faces numbered $0, 1, 7, 3, 5$ and $9$. If it is thrown, the probability of getting an odd number is
Question 8 :
A pair of dice is thrown once The probability that the sum of the outcomes is less than 11 is
Question 9 :
The probability of guessing the correct answer to a certain test is $\displaystyle\frac{x}{2}$. If the probability of not guessing the correct answer to this questions is $\displaystyle\frac{2}{3}$, then $x$ is equal to ______________.
Question 10 :
If $P(A) = \dfrac{5}{9}$, then the odds against the event $A$ is
Question 11 :
The probability of an event $A$ lies between $0$ and $1$, both inclusive. Which mathematical expression best describes this statement?<br/>
Question 12 :
If the probability of the occurrence of an event is P then what is the probability that the event doesn't occur.
Question 13 :
If the odd in favour of an event are $4$ to $7$, find the probability of its no occurence.
Question 14 :
A pair of dice is thrown. Find the probability of getting a sum of $8$ or getting an even number on both the dices.
Question 15 : A coin is tossed $400$ times and the data of outcomes is below:<span class="wysiwyg-font-size-medium"> <span class="wysiwyg-font-size-medium"><br/><table class="wysiwyg-table"><tbody><tr><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">Outcomes </p></td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$H$</p></td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$T$</p></td></tr><tr><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">Frequency</p></td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$280$</p></td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$120$</p></td></tr></tbody></table><p><br/></p><p>Find:</p><p>(i) $P(H)$, i.e., probability of getting head</p><p>(ii) $P (T)$, i.e., probability of getting tail. </p><p>(iii) The value of $P (H) + P (T)$.</p>
Question 16 :
What is the maximum value of the probability of an event?
Question 17 :
Vineeta said that probability of impossible events is $1$. Dhanalakshmi said that probability of sure events is $0$ and Sireesha said that the probability of any event lies between $0$ and $1$.<br>in the above, with whom will you agree?
Question 18 :
A bulb is taken out at random from a box of 600 electricbulbs that contains 12 defective bulbs. Then theprobability of a non-defective bulb is
Question 19 :
If the events $A$ and $B$ mutually exclusive events such that $P(A)=\dfrac {1}{3}(3x+1)$ and $P(B)=\dfrac {1}{4}(1-x)$, then the aet of possible values of $x$ lies in the interval:
Question 20 :
If I calculate the probability of an event and it turns out to be $7$, then I surely know that<br/>
Question 21 :
According to the property of probability, $P(\phi) = 0$ is used for <br>
Question 23 :
Out of the digits $1$ to $9$, two are selected at random and one is found to be $2$, the probability that their sum is odd is
Question 24 :
Ticket numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5 ?
Question 25 :
The probability expressed as a percentage of a particular occurrence can never be
Question 26 :
A biased coin with probability $p , 0 < p < 1 ,$ of heads is tossed until a head appears for thefirst time. If the probability that the number of tosses required is even, is $2 / 5 ,$ then $p$ equal to
Question 27 :
One hundred identical coins each with probability p as showing up heads are tossed. If $0 < p < 1$ and the probability of heads showing on 50 coins is equal to that of heads on 51 coins, then the value of p is
Question 28 :
A bag contains 5 blue and 4 black balls. Three balls are drawn at random. What is the probability that 2 are blueand 1 is black?
Question 30 :
A box contains $9$ tickets numbered $1$ to $9$ inclusive. If $3$ tickets are drawn from the box without replacement. The probability that they are alternatively either {odd, even, odd} of {even, odd, even} is
Question 32 :
$H$ is one of the $6$ horses entered for a race and is to be ridden by one of the two jokeys A and B. It is $2$ to $1$ that $A$ rides $H$ in which case all the horses are likely to win. If $B$ rides $H$, his chance is trebled. Then the odds against H winning is
Question 33 :
Cards are drawn one-by-one without replacement from a well shuffled pack of 52 cards. Then the probability that aface card (Jack, Queen or King) will appear for the first time on the third turn is equal to
Question 34 :
What are the odds in favour of throwing at least 8 in a single throw with two dice?
Question 35 : The table below shows the relative investment in alternative energy sources by type. One column shows the relative investment in $2007$ of $\$75$ million total invested in alternative energy. The other column shows the projected relative investment in $2017$ given current trends. The total projected investment in alternative energy in $2017$ is $\$254$ million.<br/><table class="wysiwyg-table"><tbody><tr><td></td><td>Actual $2007$ Investment</td><td>Projected 2017 Investment</td></tr><tr><td>Biofuels</td><td>0.310</td><td>0.34</td></tr><tr><td>Wind<br/></td><td>0.40</td><td>0.32</td></tr><tr><td>Solar<br/></td><td>0.27</td><td>0.30</td></tr><tr><td>Fuel Cells<br/></td><td>0.02</td><td>0.04</td></tr><tr><td>Toatl</td><td>1.00</td><td>1.00</td></tr></tbody></table>Based on the information in the table, if an investment was made in alternative energy in $2007$, what is the probability that the money was invested in wind resources?
Question 36 :
A problem in statistics is given to three students A, B and C whose chances of solving it independently are $\dfrac{1}{2}, \dfrac{1}{3}$ and $\dfrac{1}{4}$ respectively. The probability that the problem will be solved is
Question 37 :
A gumball machine contains $40$ blue gum balls, $20$ red gumballs, $15$ gumballs, and $25$ purple gumballs. What is the probability that a person gets a red gumball?
Question 38 :
Three different numbers are selected at random from the set $A = \{1,2,3, ...... 10 \}$. The probability that the product of two of the numbers is equal to third is :<br/>
Question 39 :
If $a$ and $b$ are chosen randomly from the set consisting of numbers $1,\ 2,\ 3,\ 4,\ 5,\ 6$ with replacement. Then the probability that $\displaystyle \lim _{ x\rightarrow 0 }{ { \left[ \left( { a }^{ x }+{ b }^{ x } \right) /2 \right] }^{ 2/x }=6 }$ is
Question 40 :
What are the odds in favour of throwing at least $8$ in a single throw with two dice?<br>
Question 41 :
There are three events $A$, $B$ and $C$ out of which one and only one can happen. The odds are $7$ to $3$ against $A$ and $6$ to $4$ against $B$. The odds against C are
Question 42 :
The probability of atleast one double six being thrown in $n$ thrown with two ordinary dice is greater than $99$%.<br>Then, the least numerical value of $n$ is
Question 43 :
A determinant is chosen at random from the set of all departments of order 2 with elements 0 and 1 only. The probability that the determinant chosen is non-zero is :
Question 44 :
The sum of the probabilities of the distinct outcomes within a sample space is
Question 45 :
One of the two events must happen. Given that the chance of one is two-third of the other, the odds in favor of the other are
Question 46 :
The odds in favor of standing first of three students appearing in an examination are $1:2,2:5$ and $1:7$ respectively. The probability that either of them will stand first, is
Question 47 :
If a positive integer $n$ is picked at random from the positive integers less than or equal to $10$, what is the probability that $5n + 3 \leq 14$  ?
Question 48 :
One of the two events, A and B must occur. If $P\left ( A \right )=\dfrac{2}{3}P\left ( B \right ),$ the odds in favour of $B$ are
Question 49 :
There are 5 letters and 5 different envelopes. The number of ways in which all the letters can be put in wrong envelope, is.
Question 50 :
$(a)$ The probability that it will rain tomorrow is $0.85$. What is the probability that it will not rain tomorrow?<br><br>$(b)$ If the probability of winning a game is $0.6$, what is the probability of losing it?
Question 51 :
$A$ and $B$ are two events. Odds against $A$ and $2:1$. Odds in favor of $A\cup B$ are $3:1$. If $x\le P\left( B \right) \le y$, then the ordered pair $(x,y)$ is
Question 52 :
A woman has 10 keys out of which only one opens a lock She tries the keys one after the another(keeping aside the failed ones) till she suceeds in opening the lock. What is the chance that it is the seventh key that works?
Question 53 :
A problem in statistics is given to three students whose chance of solving it are $ \dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{4}$ respectively. The probability that the question is solved is
Question 54 :
If two letters are taken at random from the word HOME, what is the probability that none of the letters would be vowels?<br/>
Question 55 :
Let $A$ and $B$ be two events with $P(A) = \dfrac {1}{3}, P(B) = \dfrac {1}{6}$ and $P(A\cap B) = \dfrac {1}{12}$. What is $P(B|\overline {A})$ equal to?
Question 56 :
A die is rolled. If the outcome is an odd number, what is the probability that it is prime?
Question 57 :
The odds against the occurrence of an event are <span class="MathJax_Preview"><span class="MJXp-math"><span class="MJXp-mn">5<span class="MJXp-mo">:<span class="MJXp-mn">4<span class="MathJax MathJax_Processed"><span class="math"><span class="mrow"><span class="mn">5<span class="mo">:<span class="mn">4 The probability of its occurrence is?
Question 58 :
A family is going to choose two pets at random from among a group of four animals: a cat, a dog, a bird, and a lizard. Find the probability that the pets that the family chooses will include the lizard.
Question 59 :
In a race, the odds in favour of horses $A, B, C, D$ are $1:3, 1:4, 1:5$ and $1:6$ respectively. Find probability that one of them wins the race.
Question 60 :
A die is thrown once.find the probability of getting a prime number less than $5.$
Question 61 :
$A, B$ are two events of a simple space.Assertion (A):- $A, B$ are mutually exclusive $\Rightarrow P\left ( A \right )\leq P\left ( \bar{B} \right )$Reason (R):- $A, B$ are mutually exclusive  $\Rightarrow P\left ( A \right )+ P\left ( B \right )\leq 1$
Question 62 :
If the odd in favour of an event are $4$ to $7$, find the probability of its occurrence.
Question 63 :
A bag contains $15$ cabbages, $20$ carrots, and $25$ turnips. If a single vegetable is picked at random from the bag, what is the probability that it will not be a carrot?
Question 64 :
If $10$% of the attacking a air crafts are expected to be shot down before reaching the target, the probability that out of $5$ aircrafts atleast four will be shot before they reach the target is
Question 65 :
In a tennis tournament, the odds that player A will be the champion is 4 to 3 and the odds that player B will be champion is 1 to 4. What are the odds that either A or B will become the champion?
Question 66 :
In a given race, the odds in favour of four horses $A, B, C$ & $D$ are $1 : 3, 1 : 4, 1 : 5$ and $1 : 6$ respectively. Assuming that a dead heat is impossible, find the chance that one of them wins the race<br/>
Question 67 :
An integer is chosen at random between 1 and 100. Find the probability that it is divisible by 8.<br/>
Question 68 :
The chance of an event happening is the square of the chance of a second event but the odds against the first are the cubes of the odds against the second. The chance of happening of each event are
Question 69 :
Two dice are tossed. What is the probability that neither die is a $4$?
Question 70 :
A bag contains $12$two rupees coins, $7$one rupee coins and $4$half rupee coins If $3$coins are selected at random, find the probability that:
Question 71 :
$n$ is an integer chosen at random from the set $\{2,5,6 \}$ and $p$ another integer chosen at random from the set $\{6,9,10 \}$. What is the probability that the two numbers $n$ and $p$ are even?
Question 72 :
The probability that atleast one of the events A and B occurs, is $0.6$. If A and B occur simultaneously with probability $0.2$, then $P(\bar{A})+P(\bar{B})$ is equal to?
Question 73 :
Four positive integers are taken at random and are multiplied together. Then the probability that the product ends in an odd digit other than 5 is
Question 74 :
If the odds in favour of winning a race by three horses are $1 : 4, 1 : 5$ and $1 : 6$, find the probability that exactly one of these horses will win.
Question 75 :
A missile target may be at a point P with probability$\displaystyle \frac{9}{10}$ or at a point Q with probability$\displaystyle \frac{1}{10}$ we have 20 shells each of which can be fired either at point P or Q Each shell may hit the target independently of the other shoot with probability$\displaystyle \frac{2}{3}$ Then number of shells must be fired at point P to hit any target with maximum probability is
Question 76 :
If $A$ and $B$ are two events such that $ P(A)=\displaystyle \frac{1}{4} $ and $P(B)= P$, the value of $P$ is not ______, if  $A\subset B$.
Question 77 :
The odds is favour of winning a race for three horses $A, B$ and $C$ respectively $1:2, 1:3$ and $1:4$. Find the probability for winning of any one of them.
Question 78 :
A number is chosen at random from the numbers $10$ to $99$. By seeing the number a man will laugh if product of the digits is $12$. If he choose three numbers with replacement then the probability that he will laugh at least once is
Question 79 :
The chance of one event happening is the square of the chance of a $2^{nd}$ event, but odds against the first are the cubes of the odds against the 2nd. Find the chances of first event. (Assume that both events are neither sure nor impossible)<br/>
Question 80 :
A number is randomly selected from the set $\left \{6, 7, 8, 8, 8, 10, 10, 11\right \}$. Find the probability the number will be less than the mean.
Question 81 :
If odds against solving a question by three students are $2:1, 5:2$ and $5:3$ respectively, then probability that the question is solved only by one students is
Question 82 :
For two events $A$ and $B , P ( B ) = P ( B / A ) = 1 / 3$ and $P ( A / B ) = 4 / 7 ,$ then <br>Option a : $P \left( B ^ { \prime } / A \right) = 2 / 3$<br>Option b : $P \left( A / B ^ { \prime } \right) = 3 / 7$<br>Option c : $A$ and $B$ are mutually exclusive<br>Option d: $A$ and $B$ are independent
Question 83 :
The odds that a book will be favorably reviewed by three independent critics are $5$ to $2,$ $4$ to $3$ and $3$ to $4$ respectively. What is the probability that of the three reviews a majority will be favorable?<br/>
Question 84 :
A man and his wife appear for an interview for two posts. The probability of the man's selection is $\dfrac{1}{5}$ and that of his wife selection is $\dfrac{1}{7}$. The probability that at least one of them is selected, is:
Question 85 :
Each of a and b can take values 1 or 2 with equal probability. The probability that the equation $ax^2 + bx + 1 = 0$ hasreal roots, is equal to
Question 86 :
X and Y plays a game in which they are asked to select a number from $21-50$. If the two number match both of them wins a prize. Find the probability that they will not win a prize in the single trial.
Question 87 :
There are two events $A$ and $B$. If odds against $A$ are as $2:1$ and those in favour of $ A \cup B$ are $3:1$ , then
Question 88 :
A fair coin is tossed five times. Calculate the probability that it lands head-up at least twice.
Question 89 :
The probability that an electronic device produced by a company does not function properly is equal to $0.1$. If $10$ devices are bought, then the probability, to the nearest thousandth, than $7$ devices function properly is
Question 90 :
In a set of games it is $3$ to $5$ in favour of the winner of the previous game.. Then the probability that a person who has won the first game shall win at least $2$ out of the next $5$ games is ?
Question 91 :
A fair coin is flipped $5$ times.<br/> The probability of getting more heads than tails is $\dfrac{1}{2}$<br/><br/>
Question 92 :
There are two bags $A$ and $B$. Bag A contains $3$ white and $4$ red balls whereas bag $B$ contains $4$ white and $3$ red balls. Three balls are drawn at random (without replacement) from one of the bags and are found to be two white and one red. Find the probability that these were drawn from bag $B$.
Question 93 :
In a group of $13$ cricket players, four are bowlers. Find out in how many ways can they form a cricket team of $11$ players in which atleast $2$ bowlers are included.
Question 94 :
A party of $23$ persons take their seats at a round table. The odds against two specified persons sitting together is
Question 95 :
There are only three events $A,B,C$ one of which must and only one can happen; the odds are $8$ to $3$ against $A,5$ to $2$ against $B$; find the odds against $C$
Question 96 :
A coin whose faces are marked 3 and 5 is tossed 4 times; what are the odds against the sum of the numbers thrown being less than 15?<br>
Question 97 :
In throwing $3$ dice, the probability that atleast $2$ of the three numbers obtained are same is
Question 98 :
If $2$ cards are drawn from a pack of $52$, then the probability that they are from the same suit is___
Question 99 :
There are four letters and four addressed envelopes. The probability that all letters are not dispatched in the right envelope is:<br/>
Question 100 :
The chance of an event happening is the square of the chance, of a second event but the odds against the first are the cubes of the odds against thefirst are the cubes of the odds against the second. Find the chance of each.
