Question 1 :
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 2 :
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 3 :
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 4 :
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 5 :
A pair of dice is thrown once The probability that the sum of the outcomes is less than 11 is

Question 6 :
A coin is tossed $400$ times and the data of outcomes is below:<span class="wysiwyg-font-size-medium">&#160;<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&#160;</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.&#160;</p><p>(iii) The value of $P (H) + P (T)$.</p>

Question 8 :
The probability of an event happening and&#160;the probability of the same event not happening (or the&#160;complement) must be a <br/>

Question 9 :
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 10 :
If the probability of the occurrence of an event is P then what is the probability that the event doesn't occur.

Question 11 :
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 12 :
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 13 :
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 14 :
A die is thrown once.find the probability of getting a prime number less than $5.$

Question 15 :
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 16 :
One of the two events, A and B must occur. If&#160;$P\left ( A \right )=\dfrac{2}{3}P\left ( B \right ),$ the odds in favour of $B$ are

Question 17 :
A card is drawn from an ordinary pack of $52$ cards and a gambler bets that it is a spade or an ace. What are the odds against his winning the bet?<br/>

Question 18 :
What is the condition if the sample space is finite and an event is $S =$ {$x_1, x_2...x_n$} then<br/>

Question 19 :
In a ODI cricket match, probability of loosing the game is&#160;$\dfrac{1}{4}$. What is the probability of winning the game ?

Question 20 :
$H$ 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 21 :
If $2$ cards are drawn from a pack of $52$, then the probability that they are from the same suit is___

Question 22 :
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 23 :
A party of $23$ persons take their seats at a round table. The odds against two specified persons sitting together is

Question 24 :
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 25 :
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: