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 fair die is thrown until a score of less than $5$ points obtained. The probability of obtaining not less than $2$ points on the last thrown is
  1. $\displaystyle\frac { 3 }{ 4 } $
  2. $\displaystyle\frac { 5 }{ 6 } $
  3. $\displaystyle\frac { 4 }{ 5 } $
  4. $\displaystyle\frac { 1 }{ 2 } $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The stopping score is uniformly one of 1, 2, 3, or 4, because the process stops at the first score below 5. Three of these four possible final scores are at least 2, so the probability is 3/4.

Multiple choice

There are $44$ students in class $X$ of a school of whom $32$ are boys and $12$ are girls. The class teacher has to select one student as a class representative. He writes the name of each student on a separate card, the cards being identical. Then he puts cards in a bag and stir them thoroughly. He then draws one card from the bag. What is the probability that the name written on the card is the name of a girl?
  1. $\dfrac{1}{11}$
  2. $\dfrac{5}{11}$
  3. $\dfrac{7}{11}$

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

Total students = 44. Girls = 12. Probability = 12/44 = 3/11. Since 3/11 is not listed in the options, 'None of these' is correct.

Multiple choice

Cards bearing numbers $3$ to $19$ are put in a box and mixed thoroughly. A card is drawn from the box at random. Find the probability that the number on the card drawn is $(i)$ Even $(ii)$ A prime $(iii)$ Divisible by $2$ and $3$ both.
  1. $(i)\quad \displaystyle\frac{2}{15}\\(ii)\quad \displaystyle\frac{1}{13}\\(iii)\quad \displaystyle\frac{3}{11}$
  2. $(i)\quad \displaystyle\frac{11}{18}\\(ii)\quad \displaystyle\frac{9}{13}\\(iii)\quad \displaystyle\frac{3}{19}$
  3. $(i)\quad \displaystyle\frac{8}{17}\\(ii)\quad \displaystyle\frac{7}{17}\\(iii)\quad \displaystyle\frac{3}{17}$

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

Numbers 3 to 19: count = 17. (i) Even: 4, 6, 8, 10, 12, 14, 16, 18 (8 numbers). Prob = 8/17. (ii) Prime: 3, 5, 7, 11, 13, 17, 19 (7 numbers). Prob = 7/17. (iii) Divisible by 2 and 3 (i.e., 6): 6, 12, 18 (3 numbers). Prob = 3/17.

Multiple choice

A bag contains 2 black, 4 white and 3 red balls. One ball is drawn at random from the bag and kept aside. From the remaining balls another ball is drawn and kept aside the first. This process is repeated till all the balls are drawn. Then probability that the balls drawn are in sequence of 2 black, 4 white and 3 red is
  1. $\displaystyle \frac {1}{1260}$
  2. $\displaystyle \frac {1}{7560}$
  3. $\displaystyle \frac {1}{210}$

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

Total balls = 9. The probability of picking the sequence (2 black, 4 white, 3 red) is (2/9 * 1/8) * (4/7 * 3/6 * 2/5 * 1/4) * (3/3 * 2/2 * 1/1). This simplifies to (2/72) * (24/840) * 1 = (1/36) * (1/35) = 1/1260.

Multiple choice

Two cubes have their faces painted either red or blue. The first cube has five red faces and one blue face. When the two cubes are rolled simultaneously, the probability that the two top faces show the same colour is 1/2. Number of red faces on the second cube, is
  1. $1$
  2. $2$
  3. $3$
  4. $4$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Cube 1: 5 red, 1 blue. Cube 2: x red, (6-x) blue. P(same color) = P(RR) + P(BB) = (5/6 * x/6) + (1/6 * (6-x)/6) = 1/2. (5x + 6 - x) / 36 = 1/2. 4x + 6 = 18. 4x = 12. x = 3.

Multiple choice

A pair of fair dice is tossed. Find the probability that the maximum of the two numbers is greater than $4$.
  1. $\dfrac{5}{9}$
  2. $\dfrac{4}{9}$
  3. $\dfrac{2}{9}$

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

The total outcomes for two dice are 36. The outcomes where the maximum is <= 4 are (1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4), which is 16 outcomes. The probability of max <= 4 is 16/36 = 4/9. Therefore, the probability of max > 4 is 1 - 4/9 = 5/9.

Multiple choice

Two dice are thrown. The probability that the sum of the numbers coming up on them is $9$, if it is known that the number $5$ always occurs on the first die, is
  1. $\displaystyle \frac { 1 }{ 6 } $
  2. $\displaystyle \frac { 1 }{ 3 } $
  3. $\displaystyle \frac { 1 }{ 2 } $
  4. $\displaystyle \frac { 5 }{ 6 } $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Sample space given 5 on first die: (5,1), (5,2), (5,3), (5,4), (5,5), (5,6). Total = 6. Favorable outcome for sum 9: (5,4). Probability = 1/6.

Multiple choice

There are $2$ groups of subjects one of which consists of $5$ science subjects & $3$ engg. subjects & other consists of $3$ science & $5$ engg. subjects. An unbiased die is cast. If the number $3$ or $5$ turns up a subject is selected at random from first group, otherwise the subject is selected from $2^{nd}$ group. Find the probability that an engg. subject is selected.
  1. $\dfrac{13}{24}$
  2. $\dfrac18$
  3. $\dfrac{5}{12}$
  4. $\dfrac{11}{24}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

P(Group 1) = P(3 or 5) = 2/6 = 1/3. P(Group 2) = 1 - 1/3 = 2/3. P(Eng | G1) = 3/8. P(Eng | G2) = 5/8. P(Eng) = (1/3 * 3/8) + (2/3 * 5/8) = 3/24 + 10/24 = 13/24.