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

There are $3$ red, $3$ white and $3$ green balls in a bag. One ball is drawn at random from a bag: $P$ is the event that ball is red. $Q$ is the event that ball is not green. $R$ is the event that ball is red or white. $S$ is the sample space. Which of the following options is correct?
  1. $n(S) = 9, n(P) =3, n(Q) = 6, n(R) = 6$
  2. $n(S) = 4, n(P) =3, n(Q) = 6, n(R) = 6$
  3. $n(S) = 6, n(P) =3, n(Q) = 6, n(R) = 6$
  4. $n(S) = 7, n(P) =3, n(Q) = 6, n(R) = 6$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total balls = 9. S = {all balls}, n(S) = 9. P = {red}, n(P) = 3. Q = {not green} = {red, white}, n(Q) = 6. R = {red or white}, n(R) = 6. All match option A.

Multiple choice

A pair of dice is thrown $7$ times. If getting at total of $7$ is considered a success, what is the probability of getting at most $6$ successes?
  1. ${ \left( \cfrac { 5 }{ 6 } \right) }^{ 7 }$
  2. ${ \left( \cfrac { 1 }{ 6 } \right) }^{ 7 }$
  3. $1-{ \left( \cfrac { 1 }{ 6 } \right) }^{ 7 }$

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The probability of getting a sum of 7 with two dice is 6/36 = 1/6. This is a binomial distribution problem with n=7, p=1/6, q=5/6. The probability of at most 6 successes is 1 minus the probability of 7 successes, which is 1 - (1/6)^7.

Multiple choice

A bag $A $ contains $3$ white and $2$ black balls and another bag $B$ contains $2$ white and $4$ black balls. $ A$ bag and a ball out of it are picked at random. What is the probability that the ball is white?
  1. $\displaystyle \frac{14}{15}$
  2. $\displaystyle \frac{8}{15}$
  3. $\displaystyle \frac{1}{15}$
  4. $\displaystyle \frac{7}{15}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

P(A) = 1/2, P(B) = 1/2. P(White|A) = 3/5. P(White|B) = 2/6 = 1/3. Total P(White) = P(A)*P(White|A) + P(B)*P(White|B) = (1/2 * 3/5) + (1/2 * 1/3) = 3/10 + 1/6 = (9+5)/30 = 14/30 = 7/15.

Multiple choice

A person throws two dice, one the common cube and the other a regular tetrahedron, the number on the lowest face being taken in the case of the tetrahedron. What is the chance that the sum of the numbers thrown is not less than 5?
  1. $\displaystyle \frac{18}{24}=\frac{3}{4}$
  2. $\displaystyle \frac{6}{24}=\frac{1}{4}$
  3. $\displaystyle \frac{6}{18}=\frac{1}{3}$
  4. $\displaystyle \frac{12}{18}=\frac{2}{3}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A cube has 6 faces (1-6). A tetrahedron has 4 faces (1-4). Total outcomes = 6 * 4 = 24. Sum < 5: (1,1), (1,2), (1,3), (2,1), (2,2), (3,1). Total 6 outcomes. Sum >= 5 = 24 - 6 = 18. Probability = 18/24 = 3/4.