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 4 red balls, 5 blue balls, and 6 green balls. If three balls are drawn completely at random from the bag, what is the mathematical probability that all three drawn balls are of identical color?

  1. 34/455

  2. 34/91

  3. 22/455

  4. 12/455

  5. 4/91
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The total number of balls is 15. The number of ways to choose 3 balls is C(15,3) = 455. The number of ways to pick 3 red is C(4,3)=4, 3 blue is C(5,3)=10, and 3 green is C(6,3)=20. The total favorable outcomes are 4+10+20 = 34, so the probability is 34/455.

Multiple choice

Directions: The question given below is followed by two statements I and II. You have to identify which statement(s) is/are sufficient to answer the question and mark the appropriate option. In how many ways can two different kinds of balls be picked from a bucket containing 15 balls? I. The bucket contains red and white balls in the ratio of 1 : 2. II. All the white balls are identical and none of the red balls is identical.

  1. Statement I alone is sufficient to answer the question.

  2. Statement II alone is sufficient to answer the question.

  3. Both the statements together are sufficient to answer the question.

  4. Both the statements together are insufficient to answer the question.

  5. Either of the statements alone is sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I gives the ratio of red to white balls (1:2), meaning 5 red and 10 white. Statement II says white are identical and red are not. To pick two different kinds of balls, we need one red and one white. Since white are identical, there is only 1 way to pick a white ball. Since red are not identical, there are 5 ways to pick a red ball. Total ways = 5 * 1 = 5. Both statements are needed.

Multiple choice

A box contains identical balls in three different colors - Black, white and blue. There are 8-x blue balls and 2X+5 black balls. If a ball is picked at random from the box, what is the probability that the ball is either blue or black? 1) X=2 2) There are 3X+39 white balls in the box.

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient

  3. BOTH statements (1) and (2) TOGETHER are sufficient to answer

  4. EACH statement ALONE is sufficient to answer the question asked

  5. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

In a certain experiment, a biased coin is tossed 80 times. The probability of the coin landing on heads in any single toss is p, where 0 p < 1. What is the probability that the coin lands on heads at least once during these 80 tosses? (1) The probability that the coin lands on tails in a single toss is 0.40. (2) In a large number of tosses, the coin lands on heads approximately 60 percent of the time.

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Probability of heads at least once = 1 - P(no heads). P(no heads) = (1-p)^80. Statement (1) says P(tails) = 0.4, so p = 0.6. This is sufficient. Statement (2) says p = 0.6 in the long run, which is also sufficient.