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Probability Quiz 11

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Probability Quiz 11

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Probability is one of important topic in Quantitative Aptitude Section. In Probability Quiz 11 article candidates can find questions with answer. By solving this questions candidates can improve and maintain, speed, and accuracy in the exams. Probability Quiz 11 questions are very useful for different exams such as IBPS PO, Clerk, SSC CGL, SBI PO, NIACL Assistant, NICL AO, IBPS SO, RRB, Railways, Civil Services etc.

shape Q1

A box contains tickets numbered from 1 to 24. 3 tickets are to be chosen to give 3 prizes. What is the probability that at least 2 tickets contain a number which is multiple of 3?
    A. [latex]\frac {35}{256}[/latex] B. [latex]\frac {33}{220}[/latex] C. [latex]\frac {63}{253}[/latex] D. [latex]\frac {43}{190}[/latex]

From 1 to 24, there are 8 numbers which are multiple of 3
Case 1: 2 are multiple of 3, and one any other number from (24 - 8) = 16 tickets
[latex]\frac {^{8}{C}_{2} \times ^{16}{C}_{1}}{^{24}{C}_{3}} = \frac {56}{253}[/latex]
Case 2: all are multiples of 3.
[latex]\frac {^{8}{C}_{3}}{^{24}{C}_{3}} = \frac {7}{253}[/latex]
Add both cases.
[latex] \frac {56}{253} + \frac {7}{253} = \frac {63}{253}[/latex]

shape Q2

A box contains 6 blue, 5 green and 4 red balls. Two balls are drawn at random. What is the probability that there is no red ball?
    A. [latex]\frac {3}{30}[/latex] B. [latex]\frac {11}{21}[/latex] C. [latex]\frac {5}{18}[/latex] D. [latex]\frac {11}{23}[/latex]

Total balls = 15
Not red means green or blue i.e. any of (5 + 6) = 11 balls
So prob. = [latex]\frac {^{11}{C}_{2}}{^{15}{C}_{2}} = \frac {11}{21}[/latex]

shape Q3

From a pack of 52 cards, 2 cards are drawn at random. What is the probability that both cards are black card or heart card?
    A. [latex]\frac {31}{102}[/latex] B. [latex]\frac {21}{73}[/latex] C. [latex]\frac {1}{5}[/latex] D. [latex]\frac {17}{100}[/latex]

Prob. of black card:
[latex]\frac {^{26}{C}_{2}}{^{52}{C}_{2}} = \frac {25}{102}[/latex]
Prob. of heart card:
[latex]\frac {^{13}{C}_{2}}{^{52}{C}_{2}} = \frac {3}{51}[/latex]
Add both cases.
[latex]\frac {25}{102} + \frac {3}{51} = \frac {31}{102}[/latex]

shape Q4

Two cards are drawn at random from a pack of 52 cards. What is the probability that either both are black or both are jacks?
    A. [latex]\frac {62}{221}[/latex] B. [latex]\frac {21}{312}[/latex] C. [latex]\frac {5}{21}[/latex] D. [latex]\frac {55}{221}[/latex]

There are total 26 cards black, and 4 jacks in which 2 are black jacks
So case 1: both are black [latex]\frac {^{26}{C}_{2}}{^{52}{C}_{2}}[/latex]
case 2: both are jack [latex]\frac {^{4}{C}_{2}}{^{52}{C}_{2}}[/latex]
Add both cases.
But now 2 black jacks have been added in both cases, so subtracting their prob. : [latex]\frac {^{2}{C}_{2}}{^{52}{C}_{2}}[/latex]
So [latex]\frac {325}{1326} + \frac {6}{1326} – \frac {1}{1326} = \frac {55}{221}[/latex]

shape Q5

From a group of 3 men, 4 women and 2 children, 4 people are to be chosen to form a committee. What is the probability that the committee contains 1 each of men, women and children?
    A. [latex]\frac {4}{15}[/latex] B. [latex]\frac {12}{21}[/latex] C. [latex]\frac {4}{19}[/latex] D. [latex]\frac {11}{31}[/latex]

Case 1: Prob. when 2 men, 1 woman and 1 child [latex]\frac {^{3}{C}_{2} \times ^{4}{C}_{1} \times ^{2}{C}_{1}}{^{9}{C}_{4}} = \frac {4}{21}[/latex]
Case 2: Prob. when 1 man, 2 women and 1 child [latex]\frac {^{3}{C}_{1} \times ^{4}{C}_{2} \times ^{2}{C}_{1}}{^{9}{C}_{4}} = \frac {2}{7}[/latex]
Case 3: Prob. when 1 man, 1 woman and 2 children [latex]\frac {^{3}{C}_{1} \times ^{4}{C}_{1} \times ^{2}{C}_{2}}{^{9}{C}_{4}} = \frac {2}{21}[/latex]
Add three cases
[latex]\frac {4}{21} + \frac {2}{7} + \frac {2}{21} = \frac {12}{21}[/latex]

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