Question 2 :
If a coin is tossed twice, find the probability of getting at least one head.
Question 3 : A survey was conducted by car manufacturing company in a metropolitan city on $1000$ persons having monthly income from Rs. $30,001$ to Rs. $50,000$. The data about the number of persons in various categories is as under:<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-right">Monthly income</p><span class="wysiwyg-font-size-medium"><br/> </td><td colspan="3"><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">Number of Cars</p><span class="wysiwyg-font-size-medium"><br/> </td></tr><tr><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">(in rupees)</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$1$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$2$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">More than $2$</p><span class="wysiwyg-font-size-medium"><br/> </td></tr><tr><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-right">$30,001-40,000$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-right">$400$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$50$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$25$</p><span class="wysiwyg-font-size-medium"><br/> </td></tr><tr><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-right">$40,001-50,000$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-right">$100$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$300$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$125$</p><span class="wysiwyg-font-size-medium"><br/> </td></tr></tbody></table> Find the probability that a person selected at random in the income slab $40,001-50,000$ have more than $2$ cars.
Question 4 :
If a coin is tossed, then the probability that a head turns up is ______.
Question 5 :
A die is tossed $80$ times and the number $3$ is obtained $14$ times. Now, a dice is tossed at random, then the probability of getting the number $3$ is ________.
Question 6 : <p>There are $40$ students in a class and their results is presented as below :</p><table class="wysiwyg-table"><tbody><tr><td>Result (Pass/Fail)</td><td>Pass</td><td>Fail</td></tr><tr><td>Number of Students</td><td>$30$</td><td>$10$</td></tr></tbody></table><p></p><p>If a student chosen at random out of the class, find the probability that the student has passed the examination.</p>
Question 7 :
The probability that a two digit number selected at random will be a multiple of '$3$' and not a multiple of '$5$' is<br/>
Question 8 :
A box has tokens numbered 3 to 100. If a token is taken out at random the chance that the number is divisible by 7 is
Question 9 :
In a non-leap year the probability of getting $53$ Sundays or $53$ Tuesdays or $53$ Thursdays is.
Question 10 :
A coin is tossed. What is the probability of getting a head and a tail?
Question 11 :
Two men hit at a target with probabilities $\dfrac{1}{2}$ and $\dfrac{1}{3}$ respectively. What is the probability that exactly one of them hits the target?
Question 12 :
A card is drawn from a well shuffled deck of $52$ cards. Find the probability of getting a club card?
Question 13 : A die having six faces is tossed $80$ times and the data is as 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>Outcome</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$1$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$2$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$3$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$4$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p>$5$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-right">$6$</p><span class="wysiwyg-font-size-medium"><br/> </td></tr><tr><td><span class="wysiwyg-font-size-medium"><br/> <p>Frequency</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$10$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$20$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$10$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$28$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$8$</p><span class="wysiwyg-font-size-medium"><br/> </td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-right">$4$</p><span class="wysiwyg-font-size-medium"><br/> </td></tr></tbody></table><p>Find $P (1) $.</p>
Question 14 : <p>Fifty seeds were selected at random from each of $5$ bags $A, B, C, D, E$ of seeds, and were kept under standardised conditions equally favourable to germination. After $20$ days, the number of seeds which had germinated in each collection were counted and recorded as follow :</p><span class="wysiwyg-font-size-medium"><table class="wysiwyg-table"><tbody><tr><td>Bag</td><td>$A$</td><td>$B$</td><td>$C$</td><td>$D$</td><td>$E$</td></tr><tr><td><p>Number ofseeds</p><p>germinated</p></td><td>$40$</td><td>$48$</td><td>$42$</td><td>$39$</td><td>$41$</td></tr></tbody></table><p><span class="wysiwyg-font-size-medium"></p><p><span class="wysiwyg-font-size-medium"></p><p></p><span class="wysiwyg-font-size-medium"><p>What is the probability of germination of</p><p>$(i)$ more than $40$ seeds in a bag?</p><p>$(ii)$ $49$ seeds in a bag?</p><p>$(iii)$ more than $35$ seeds in a bag?</p><p><br></p>
Question 15 :
The probability that a leap year will have only $52$ Sundays is
Question 16 :
A die is rolled so that the probability of face $i$ is proportional to $i,\,\,\{i=1,2,.....6\}$. The probability of an even number occurring when the die is rolled, is
Question 17 :
In a World Cup final match against Srilanka, for six times Sachin Tendulkar hits a six out of $30$ balls he plays. What is the probability that in a given throw the ball does not hit a six?
Question 18 :
There are only two women among $20$ persons taking part in a pleasure trip. The $20$ persons are divided into two groups, each group consisting of $10$ persons. Then the probability that the two women will be in the same group is:
Question 19 :
What is the probability that a two digit number selected at random will be a multiple of $3$ and not a multiple of $5$?
Question 20 :
Assertion: Consider an event for which probability of success is 1/2.<br>Probability that in n trials,there are r success where r-4K and k is an integer is $\dfrac{1}{4}+\dfrac{1}{2^{n/2+1}}cos (\dfrac{n\pi}{4})$
Reason: $^nC_0+^nC_4+^nC_7+.......=2^{n/2} sin (\dfrac{n \pi}{4})$
Question 21 : <p>A tyre manufacturing company kept a record of the distance covered before a tyre needed to be replaced. The table show the result of $1000$ cases :</p><table class="wysiwyg-table"><tbody><tr><td>Distance in $Km$</td><td>Frequency</td></tr><tr><td>Less than $4000$</td><td>       $20$</td></tr><tr><td>$4000$ to $9000$</td><td>      $210$</td></tr><tr><td>$9000$ to $14000$</td><td>      $325$</td></tr><tr><td>More than $14000$</td><td>      $445$</td></tr></tbody></table><p>If you buy a tyre of this company what is the probability that it will need to be replaced after it has covered somewhere between $4000\, km$ and $14000\, km$?</p>
Question 22 :
From a normal pack of cards, a card is drawn at random. Find the probability of getting a jack or a king.
Question 23 :
A bag contains $14$ balls of two colours, the number of balls of colour being equal, seven balls are drawn at random one by one. The ball in hand is returned to the bag before each new draw. The probability that at least $3$ balls of each colour are drawn, is:
Question 24 :
Let ${ S }_{ n }=\displaystyle\sum _{ k=1 }^{ n }{ k }$ denote the sum of the first $n$ positive integers. The numbers ${ S }_{ 1 }, { S }_{ 2 }, { S }_{ 3 }, \dots , { S }_{ 99 }$ are written on $99$ cards. The probability of drawing a card with an even number written on it is
Question 26 : Two coins are tossed $1000$ times and the outcomes are recorded as below:<br><table class="wysiwyg-table"><tbody><tr><td>No of heads<br></td><td>$2$<br></td><td>$1$<br></td><td>$0$<br></td></tr><tr><td>Frequency<br></td><td>$200$<br></td><td>$550$<br></td><td>$250$<br></td></tr></tbody></table>Based on this information, the probability for at most one head is $\dfrac{a}{b}$. Where $(a,b)=1$, then<br>
Question 27 :
A bag contains $15$ red, $8$ blue and several green marbles. A marble is selected at random. The probability of drawing a blue marble is $\dfrac {1}{5}$. $5$ green marbles are now taken out from the bag. If a marble is now drawn at random, find the probability of drawing a green marble
Question 28 :
A box contains $40$ red and blue marbles. If a marble is drawn at random, the probability of picking a blue marble is $\dfrac {3}{8}$. Ansh takes out one red and nine blue marbles and then draws a marble at random. Find the probability of drawing a blue marble
Question 29 :
A bag contains 4 white and 2 black balls and another bag contains 3 white and 5 black balls. If one ball is drawn from each bag, then the probability that one ball is white and one ball is black is
Question 30 :
A bag contains a number of marbles of which $80$ are red, $24$ are white and the rest are blue. If the probability of randomly selecting a blue marble from this bag is $\dfrac {1}{5}$, how many blue marbles are there in the bag?
Question 31 :
What is the total number of candidates at an examination, if 31 % fail and the number of failing students is 248.
Question 32 :
A box contains $25$ tickets number $1,2,....25$. If two tickets are drawn at random then the probability that the product of their numbers is even, is
Question 33 :
Set $S$ has $4$ elements, $A$ and $B$ are subsets of $S$. The probability that$A$ and $B$ are not disjoint is
Question 34 :
A card is drawn from a well-shuffled deck of playing cards. Find the probability of drawing a face card.
Question 35 : <p>On one page of a telephone directly, there were $200$ telephone numbers. The frequency distribution of their unit place digit (for example in the number $25828573$, the unit place digit is $3$) is given in table below : </p><table class="wysiwyg-table"><tbody><tr><td>Digit</td><td>$0$</td><td>$1$</td><td>$2$</td><td>$3$</td><td>$4$</td><td>$5$</td><td>$6$</td><td>$7$</td><td>$8$</td><td>$9$</td></tr><tr><td>Frequency</td><td>$22$</td><td>$26$</td><td>$22$</td><td>$22$</td><td>$20$</td><td>$10$</td><td>$14$</td><td>$28$</td><td>$16$</td><td>$20$</td></tr></tbody></table><p>Without looking at the page, the pencil is placed on one of these numbers, i.e., the number is chosen at random. What is the probability that the digit in its unit place is more than $7$?</p>
Question 36 :
A die is thrown three times and the sum of three numbers obtained is $15$. The probability of first throw being $6$ is:
Question 37 :
Archaeological survey indicates that the odd of occurring earthquake in Greater Himalayan region due to Tehri Dam are $5$ to $7$. What is the probability of earthquake in Greater Himalayan region?
Question 38 :
A box contains coupons labeled 1, 2, 3, ... , n. A coupon is picked at random and the number x is noted. The coupon is put back into box and a new coupon is picked at random. The new number is y. Then the probability that one of the numbers x, y divides the other is : (in the options below [r] denotes the largest integer less than or equal to r)
Question 39 :
In a school, $\displaystyle \frac{5}{8}$ of the total students are girls. If the number of girls is $120$ more than that of the boys. What is the strength of the school? how many boys are there?
Question 40 :
A dies is thrown three times and the sum of three numbers obtained is $15$. The probability of first throw being $5$ is:
