Quantitative Aptitude

Probability

1,860 Questions
All Sample Space Setup 558 Permutation & Combination Counting 288 Multiplication Theorem (AND) 234 Addition Theorem (OR) 151 At Least One Probability 134 Complement Rule (P(Not A)) 130 Drawing Without Replacement 126 Conditional Probability 75 Bayes' Theorem 69 Drawing With Replacement 49 Success and Failure Rates 46

Probability Questions

Multiple choice

A bag contains $8$ red and $5$ white balls. Three balls are drawn at random. Find the probability that one ball is red and two balls are white.
  1. $\displaystyle\frac{40}{143}$
  2. $\displaystyle\frac{40}{147}$
  3. $\displaystyle\frac{41}{141}$
  4. $\displaystyle\frac{39}{147}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The total number of ways to choose 3 balls from 13 is 13C3 = 286. The number of ways to choose 1 red ball from 8 is 8C1 = 8, and 2 white balls from 5 is 5C2 = 10. The probability is (8 * 10) / 286 = 80 / 286 = 40 / 143.

Multiple choice

Four cards are drawn at random from a pack of $52$ playing cards. The probability of getting all the four cards of the same suit is
  1. $\displaystyle\frac{44}{4165}$
  2. $\displaystyle\frac{22}{4165}$
  3. $\displaystyle\frac{11}{4165}$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

There are 4 suits, each with 13 cards. The number of ways to choose 4 cards of the same suit is 4 * C(13, 4). The total ways to choose 4 cards from 52 is C(52, 4). Calculating this: 4 * (13*12*11*10 / 24) / (52*51*50*49 / 24) = 4 * 715 / 270725 = 2860 / 270725 = 44 / 4165.

Multiple choice

A coin is tossed and a die is thrown simultaneously : $P$ is the event of getting head and a odd number. $Q$ is the event of getting either $H$ or $T$ and an even number. $R$ is the event of getting a number on die greater than $7$ and a tail. $S$ is the sample space. Which of the following options is correct?
  1. $n(S) = 12, n(P) = 3, n(Q) = 2, n(R) = 0$
  2. $n(S) = 12, n(P) = 3, n(Q) = 3, n(R) = 0$
  3. $n(S) = 12, n(P) = 3, n(Q) = 6, n(R) = 0$
  4. $n(S) = 12, n(P) = 3, n(Q) = 5, n(R) = 0$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Sample space S = {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}, n(S)=12. P (Head and odd) = {H1, H3, H5}, n(P)=3. Q (H or T and even) = {H2, H4, H6, T2, T4, T6}, n(Q)=6. R (Number > 7 and Tail) = {}, n(R)=0.

Multiple choice

From each of two equal lines (of length $i$) a portion is cut off at random and removed. What is the chance that the sum of the remainders is less than $i$ ?
  1. $\displaystyle \dfrac{1}{3}$
  2. $\displaystyle \dfrac{1}{2}$
  3. $\displaystyle \dfrac{2}{3}$
  4. $\displaystyle \dfrac{1}{4}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let x and y be the lengths cut from two lines of length i. x, y are independent variables uniform on [0, i]. We want P( (i-x) + (i-y) < i ) = P( 2i - x - y < i ) = P( x + y > i ). The region x+y > i in the square [0, i]x[0, i] has area 1/2 of the total area.

Multiple choice

Two fair dice are thrown, find the probability that sum of the points on their uppermost faces is greater than $10$ or an odd number:
  1. $\displaystyle \frac{16}{36}$
  2. $\displaystyle \frac{17}{36}$
  3. $\displaystyle \frac{18}{36}$
  4. $\displaystyle \frac{19}{36}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The sum is greater than 10 if it is 11 or 12, which occurs in 3 outcomes (5,6), (6,5), (6,6). The sum is odd if it is 3, 5, 7, 9, or 11, which occurs in 18 outcomes. Using the inclusion-exclusion principle, the total favorable outcomes are 3 + 18 - 1 (since 11 is counted in both) = 20, but the question asks for the union of these sets. The sum > 10 is {11, 12} and odd sums are {3, 5, 7, 9, 11}. The union is {3, 5, 7, 9, 11, 12}, which covers 18 + 1 = 19 outcomes.