Question 1 :
In a single throw of a die, the probability of getting a multiple of $3$ is ____________.
Question 2 :
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 3 : <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 4 : There are $40$ students in a class and their results is presented as below :<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> If a student chosen at random out of the class, find the probability that the student has passed the examination<br/>
Question 5 :
What is the probability that there are $5$ Mondays in the month of February 2016?
Question 6 : <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 7 : <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>
Question 8 : 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 9 : 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 10 : <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 11 : 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 $\dfrac{a}{b}$ is<br/>
Question 12 :
A die is thrown once. The probability of getting a number $3$ or $4$ is _________.
Question 13 :
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 14 : On one page of a telephone directory there were $200$ telephone numbers. The frequency distribution of their unit place digit is given in the following table:<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>
Question 15 :
A ball is drawn at random from a box containing 10 red, 30 white, 20 blue and 15 orange marbles. The probability of a ball drawn is red, white or blue .......
Question 16 : Observe the table given.<table class="wysiwyg-table"><tbody><tr><td>Club</td><td>English</td><td>Maths</td><td>Science</td></tr><tr><td>Number of students</td><td>$99$</td><td>$121$</td><td>$154$</td></tr></tbody></table>A student is chosen randomly from the group as the co-ordinator of all the clubs. What is the probability that the student is from the science club?
Question 17 :
A pair of dies is thrown, find the probability of getting a total of numbers is more than $10$.
Question 18 : 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/></span><table class="wysiwyg-table"><tbody><tr><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-right">Monthly income</p><span class="wysiwyg-font-size-medium"><br/> </span></td><td colspan="3"><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">Number of Cars</p><span class="wysiwyg-font-size-medium"><br/> </span></td></tr><tr><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-center">(in rupees)</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">More than $2$</p><span class="wysiwyg-font-size-medium"><br/> </span></td></tr><tr><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-right">$30,001-40,000$</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">$400$</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">$50$</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">$25$</p><span class="wysiwyg-font-size-medium"><br/> </span></td></tr><tr><td><span class="wysiwyg-font-size-medium"><br/> </span><p class="wysiwyg-text-align-right">$40,001-50,000$</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">$100$</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">$300$</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">$125$</p><span class="wysiwyg-font-size-medium"><br/> </span></td></tr></tbody></table><span> </span><span>Find the probability that a person selected at random i</span><span>n the income slab $40,001-50,000$ have more than $2$ cars.</span>
Question 19 :
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 20 :
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.
