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

Out of (2n+1) tickets consecutively numbered,three are drawn at random. The chance that the numbers on them are in A.P. is
  1. $\displaystyle \frac{n}{n^{2}-1}$
  2. $\displaystyle \frac{3n}{n^{2}-1}$
  3. $\displaystyle \frac{3n}{4n^{2}-1}$
  4. $\displaystyle \frac{3n}{4n^{2}+2n-1}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The total number of ways to choose 3 tickets from 2n+1 is C(2n+1, 3). For the numbers to be in A.P., the sum of the first and third must be even, meaning they must have the same parity; there are n+1 odd and n even numbers. Calculating the favorable outcomes leads to the probability 3n / (4n^2 - 1).

Multiple choice

A coin is so biased that the probability of falling head when tossed is $\displaystyle \frac{1}{4}$ . If the coin is tossed $5$ times the probability of obtaining $2$ heads and $3$ tails, with heads occurring in succession is
  1. $\displaystyle \frac{5\times 3^{3}}{4^{5}}$
  2. $\displaystyle \frac{3^{3}}{5^{4}}$
  3. $\displaystyle \frac{3^{3}}{4^{4}}$
  4. $\displaystyle \frac{3^{3}}{4^{5}}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Probability of head p=1/4, tail q=3/4. We need 2 heads and 3 tails with heads in succession. Possible patterns: HHTTT, THHTT, TTHHT, TTTHH. There are 4 such patterns. Each pattern has probability (1/4)^2 * (3/4)^3 = 27/1024. Total probability = 4 * 27/1024 = 27/256 = 3^3 / 4^4.

Multiple choice

Two dice are thrown together. Find the probability that the two digit number formed with the two numbers turning up is divisible by $3$.
  1. $\dfrac{1}{2}$
  2. $\dfrac{1}{3}$
  3. $\dfrac{2}{3}$
  4. $\dfrac{1}{6}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

There are 36 possible outcomes when throwing two dice. The two-digit numbers formed range from 11 to 66; those divisible by 3 are 12, 15, 21, 24, 33, 36, 42, 45, 51, 54, 66 (total 12). The probability is 12/36 = 1/3.

Multiple choice

If two cards are drawn simultaneously from the same set, the probability that atleast one of them will be the ace of hearts is.
  1. $\displaystyle\frac{1}{13}$
  2. $\displaystyle\frac{1}{26}$
  3. $\displaystyle\frac{1}{52}$
  4. $\displaystyle\frac{3}{13}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The probability that neither card is the ace of hearts is (51/52) * (50/51) = 50/52 = 25/26. The probability that at least one is the ace of hearts is 1 - 25/26 = 1/26.

Multiple choice

Die A has $4$ red and $2$ white faces where as die $B$ has two red and $4$ white faces. $A$ fair coin is tossed. If head turns up, the game continues by throwing die A, if tail turns up then die B is to be used. Probability of getting a red face at any throw is
  1. $\displaystyle \frac{1}{2}$
  2. $\displaystyle \frac{2}{3}$
  3. $ \displaystyle\frac{1}{3}$

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

P(Red) = P(Red|A)P(A) + P(Red|B)P(B). P(A) = 1/2, P(B) = 1/2. P(Red|A) = 4/6 = 2/3. P(Red|B) = 2/6 = 1/3. P(Red) = (2/3 * 1/2) + (1/3 * 1/2) = 1/3 + 1/6 = 1/2.