Question 1 :
When a coin is tossed at random, then the probability of getting a head is ________.
Question 2 :
What is the probability that there are $5$ Mondays in the month of February 2016?
Question 3 :
A die having six faces is tossed $80$ times and the data is as below:<span class="wysiwyg-font-size-medium"> </span><span class="wysiwyg-font-size-medium"><br/></span><table class="wysiwyg-table"><tbody><tr><td><span class="wysiwyg-font-size-medium"><br/> </span><p>Outcome</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">$1$</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">$2$</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">$3$</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">$4$</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p>$5$</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-right">$6$</p><span class="wysiwyg-font-size-medium"><br/> </span></td></tr><tr><td><span class="wysiwyg-font-size-medium"><br/> </span><p>Frequency</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">$10$</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">$20$</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">$10$</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">$28$</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">$8$</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-right">$4$</p><span class="wysiwyg-font-size-medium"><br/> </span></td></tr></tbody></table><p>Find $P (1) $.</p>
Question 4 :
In a shooting game, John shoots the balls $20$ times out of $40$ trials. What is the empirical probability of the shooting event?<br/>
Question 5 :
<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/></span></p><span class="wysiwyg-font-size-medium"></span><table class="wysiwyg-table"><tbody><tr><td><span>            Marks <br/>           secured</span></td><td><span>Number of <br/></span>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"></span></p><p><span class="wysiwyg-font-size-medium"></span></p><p><span class="wysiwyg-font-size-medium"></span></p><p></p><span class="wysiwyg-font-size-medium"></span><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 6 :
Two men hit at a target with probabilities <span>$\dfrac{1}{2}$</span> and <span>$\dfrac{1}{3}$ </span>respectively. What is the probability that exactly one of them hits the target?
Question 7 :
A die is thrown $200$ times and the outcomes $1, 2, 3, 4, 5, 6$ have frequencies as below:<span class="wysiwyg-font-size-medium"> </span><span class="wysiwyg-font-size-medium"><br/></span><table class="wysiwyg-table"><tbody><tr><td><span class="wysiwyg-font-size-medium"><br/> </span><p><span class="wysiwyg-font-size-medium">Outcome</span></p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$1$</span></p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$2$</span></p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$3$</span><span class="wysiwyg-font-size-medium"><br/>  </span></p></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$4$</span></p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$5$</span></p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$6$</span></p><span class="wysiwyg-font-size-medium"><br/> </span></td></tr><tr><td><span class="wysiwyg-font-size-medium"><br/> </span><p><span class="wysiwyg-font-size-medium">Frequency</span></p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$40$</span></p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$38$</span></p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$43$</span></p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$29$</span></p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$28$</span></p><span class="wysiwyg-font-size-medium"><br/> </span></td><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center"><span class="wysiwyg-font-size-medium">$22$</span></p><span class="wysiwyg-font-size-medium"><br/> </span></td></tr></tbody></table><p><span class="wysiwyg-font-size-medium"><span>Find the probabilities of </span><span>getting a number more than $1$ and less than $6$ </span><span>in a toss (trial).</span><br/></span></p>
Question 8 :
<p>There are $500$ packets in a large box and each packet contains $4$ electronic devices in it. On testing, at the time of packing, it was noted that there are some faulty pieces in the packets. The data is as below:</p><table class="wysiwyg-table"><tbody><tr><td><span>No. of faulty <br/></span>devices in a packet</td><td>Number of packets</td></tr><tr><td>                 $0$</td><td>             $300$</td></tr><tr><td>                 $1$</td><td>             $100$</td></tr><tr><td>                 $2$</td><td>               $50$</td></tr><tr><td>                 $3$</td><td>               $30$</td></tr><tr><td>                 $4$</td><td>               $20$</td></tr><tr><td>Total number of packets</td><td>              $500$</td></tr></tbody></table><p>If one packet is drawn from the box, what is the probability that all the four devices in the packet are without any fault?</p>
Question 9 :
In a single throw of a die, the probability of getting a multiple of $3$ is ____________.
Question 10 :
<p>A coin is tossed $150$ times and the outcomes are recorded. The frequency distribution of the outcomes $H$ (i.e, head) and $T$ (i.e, tail) is given below :</p><table class="wysiwyg-table"><tbody><tr><td>Outcome</td><td>$H$</td><td>$T$</td></tr><tr><td>Frequency</td><td>$85$</td><td>$65$</td></tr></tbody></table><p><span class="wysiwyg-font-size-medium"></span></p><p>Find the value of $P(H)$, i.e, probability of getting a head in a single trial.</p>