Question 1 :
If a coin is tossed twice, find the probability of getting at least one head.
Question 2 : To know the opinion of the student about the subject<span class="wysiwyg-font-size-medium"> statistic, a survey of $200$ students was conducted.<p>The data is recorded in the following table</p><table class="wysiwyg-table"><tbody><tr><td>Opinion</td><td>Like</td><td>Dislike</td></tr><tr><td>No. of Students</td><td>$135$</td><td>$65$</td></tr></tbody></table><p>Find the probability that a student chosen at random</p><span class="wysiwyg-font-size-medium"><p></p><p></p><p></p><p>$(i)$ likes statistics, $(ii)$ does not like it.</p>
Question 3 :
Bag contains $100$ tickets bearing numbers $1-100$. A ticket is taken out randomly, find the probability getting of a even numbered ticket.<br/>
Question 4 :
A coin is tossed. What is the probability of getting a head and a tail?
Question 5 :
A coin is tossed $5$ times. The probability of $2$ heads and $3$ tails is:
Question 6 :
If $3$ coins are tossed simultaneously, the probability of $2$ heads and $1$ tail is:
Question 7 : <p>$400$ students of class $X$ of a school appeared in a test of $100$ marks in the subject of social<br/>studies and the data about the marks secured is as below :<span class="wysiwyg-font-size-medium"><br/></p><span class="wysiwyg-font-size-medium"><table class="wysiwyg-table"><tbody><tr><td>            Marks <br/>           secured</td><td>Number of <br/>Students</td></tr><tr><td>            $0-25$</td><td>     $50$</td></tr><tr><td>          $26-50$</td><td>    $220$</td></tr><tr><td>          $51-75$</td><td>    $100$</td></tr><tr><td>        Above $75$</td><td>      $30$</td></tr><tr><td>Total number of students</td><td>    $400$</td></tr></tbody></table><p><span class="wysiwyg-font-size-medium"></p><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>If the result card of a student he picked up at random, what is the probability that the student has secured more than $50$ marks.</p>
Question 8 :
If $3$ coins are tossed simultaneously, the probability of $1$ head and $2$ tails is:
Question 9 :
When two dice are thrown simultaneously the probability that the sum of the two numbers that turn up is more than $11$ is:
Question 10 :
A coin is tossed five times, find the probability of getting no head.
Question 11 :
A bag contains $6$ white and $4$ red balls. If a person draws $2$ balls and receives Rs. $10$ and Rs. $20$ for a white and red balls respectively, then his expected amount is -
Question 12 :
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 13 : <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 14 : <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 15 :
A box contains $32$ coloured marbles. $8$ of them are red marbles and the rest are either blue or green marbles. A marble is drawn at random. Calculate the probability of drawing a marble which is not red in colour.
Question 16 : A die is thrown $400$ times, the frequency of the outcomes of the events are given as under.<br/><table class="wysiwyg-table"><tbody><tr><td>outcome<br/></td><td>$1$<br/></td><td>$2$<br/></td><td>$3$<br/></td><td>$4$<br/></td><td>$5$<br/></td><td>$6$<br/></td></tr><tr><td>Frequency<br/></td><td>$70$<br/></td><td>$65$<br/></td><td>$60$<br/></td><td>$75$<br/></td><td>$63$<br/></td><td>$67$<br/></td></tr></tbody></table>Find the probability of occurrence of an odd number.<br/>
Question 17 :
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 18 :
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 19 :
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 20 : <p>Two dice are thrown. The number of sample points in the sample space when six does not appear on any one side is</p>
Question 21 :
A die is thrown three times and the sum of three numbers obtained is $15$. The probability of first throw being $6$ is:
Question 22 :
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 23 :
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 24 :
A die is thrown three times and the sum of three numbers obtained is $15$. The probability of first throw being $6$ is:
