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

In a lottery game, there are 50 main numbered balls (1 to 50), and 6 balls are randomly drawn without replacement. Additionally, there are 10 special "bonus" balls numbered 1 to 10, and 1 bonus ball is drawn separately. What is the probability of matching all 6 main numbers ball and the bonus ball in the exact order they are drawn?

  1. 1/(50 × 49 × 48 × 47 × 46 × 45 × 10)

  2. (1 × 6)/(50 × 49 × 48 × 47 × 46 × 45 × 10)

  3. (10 × 6)/(50 × 49 × 48 × 47 × 46 × 45 × 10)

  4. (50 × 6)/(50 × 49 × 48 × 47 × 46 × 45 × 10)

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

Since the balls must be matched in the exact order they are drawn, the probability of matching the first ball is 1/50, the second is 1/49, and so on, down to 1/45 for the sixth ball. The probability of matching the single bonus ball is 1/10, so the combined probability is the product of these individual probabilities.

Multiple choice

From a deck of 52 playing cards, including 4 aces, a player randomly draws 7 cards without replacement. What is the probability that exactly 2 of the seven drawn cards are aces and the remaining 5 cards are non-ace cards?

  1. 4 C 2 + 48 C 5 52 C 7

  2. 4 C 2 × 48 C 5 52 C 7

  3. 7 C 2 + 48 C 5 52 C 7

  4. 7 C 2 × 48 C 5 52 C 7

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

Choose exactly 2 of the 4 aces and 5 of the 48 non-aces, then divide by the total number of 7-card hands. The probability is C(4,2) x C(48,5) / C(52,7), corresponding to option B.

Multiple choice

Michael has two dice, each with faces labeled with the numbers -12, -8, -4, 4, 8, and 12. He rolls the two dice and adds the resulting numbers. Quantity A Probability that the sum is greater than zero Quantity B Probability that the sum is less than zero

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The set of values is {-12, -8, -4, 4, 8, 12}. Since the distribution is symmetric around zero, the probability of getting a positive sum is equal to the probability of getting a negative sum. The only case where the sum is zero is when the two dice show additive inverses (e.g., -12 and 12, or 4 and -4).

Multiple choice

A certain coin is tossed with probability of showing head being p. let q denotes the probability that when the coin is tossed four times the number of heads obtained is even then

  1. 2q= 1 +(2p-1)4

  2. q = l + (2p + 1 ) 4

  3. q = 1 - (2p - 1 )4

  4. 2q = 1 - (2p + 1 )4
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The probability of an even number of heads in n trials is given by (1 + (1-2p)^n)/2. For n=4, this is (1 + (1-2p)^4)/2. Since (1-2p)^4 = (2p-1)^4, the expression becomes (1 + (2p-1)^4)/2, or 2q = 1 + (2p-1)^4.