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

Find the probability of the first draw that gives 4 red candies and the second draw that gives 4 blue candies from a bag that contains 6 red and 9 blue candies, if two successive drawings of four candies are made, so that the candies are not replaced before second draw.

  1. 55 441

  2. 86 441

  3. 3 715

  4. 4 715

  5. 6 715
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The probability is calculated by (ways to pick 4 red from 6) * (ways to pick 4 blue from 9) / (total ways to pick 4 from 15) * (total ways to pick 4 from 11). The calculation yields 3/715.

Multiple choice

A person gets 9 balls in an event of a festival. He has to put the balls in a basket. To successfully complete the event, he must put more number of balls in the basket than the number of balls which he fails to put. How many number of ways are possible for being him unsuccessful?

  1. 1024

  2. 128

  3. 512

  4. 256

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

Total outcomes for 9 balls (each can be in or out) is 2^9 = 512. Success means balls in > balls out. Since 9 is odd, there are no ties. By symmetry, half are successes and half are failures. 512 / 2 = 256.

Multiple choice

There are 3 piles of identical red, blue and green balls and each pile contains at least 10 balls. The number of ways of selecting 10 balls, if twice as many red balls as green balls are to be selected, is

  1. 3

  2. 4

  3. 6

  4. 8
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let r, b, g be the number of red, blue, and green balls. r + b + g = 10 and r = 2g. Substituting: 2g + b + g = 10, so 3g + b = 10. Since g and b must be non-negative integers: if g=0, b=10; if g=1, b=7; if g=2, b=4; if g=3, b=1. There are 4 possible solutions.

Multiple choice

In how many ways can two dice be rolled, so that the sum of the values on the upper faces is divisible by three?

  1. 9

  2. 12

  3. 15

  4. 18
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

There are 36 total outcomes when rolling two dice. The sums divisible by 3 are 3, 6, 9, and 12. The pairs summing to 3 are (1,2), (2,1); to 6 are (1,5), (2,4), (3,3), (4,2), (5,1); to 9 are (3,6), (4,5), (5,4), (6,3); and to 12 is (6,6). Counting these gives 2 + 5 + 4 + 1 = 12 outcomes.