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 the given questions, two quantities are given, one as Quantity I and another as Quantity II. You have to determine relationship between two quantities and choose the appropriate option. A box contains 4 Red balls, 6 white balls, 2 orange balls and 8 black balls. Quantity I: Two balls are drawn at random probability that both balls are either red or white. Quantity II: Three balls are drawn. The probability that all are different.

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or No relation
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total balls = 4+6+2+8 = 20. Quantity I: P(2 Red or 2 White) = (4C2 + 6C2) / 20C2 = (6 + 15) / 190 = 21/190 approx 0.11. Quantity II: P(3 different) = (4*6*2 + 4*6*8 + 4*2*8 + 6*2*8) / 20C3 = (48 + 192 + 64 + 96) / 1140 = 400/1140 approx 0.35. Thus, I < II.

Multiple choice

If a card is drawn from a deck of cards, what is the probability of a card drawn to be a red or a black card and what can we say about that event?

  1. 1 and it is a sure event.

  2. 0 and it is a sure event.

  3. 1 and it is an impossible event. .

  4. 0 and it is an impossible event
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A card is either red or black. The probability of drawing a red or black card is 1, as every card in a standard deck is one of these two colors. This is a sure event.

Multiple choice

Three coins are tossed in the air and two of the coins land with tails face upwards. What are the chances on the next toss of the coins that at least two of the coins will land with the Heads facing upwards?

  1. 50%

  2. 25%

  3. 75%

  4. 100%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The next toss is independent of previous outcomes. For three coins, the probability of at least two heads is the probability of 2 heads (HHT, HTH, THH) or 3 heads (HHH). Total outcomes = 2^3 = 8. Favorable = 4. Probability = 4/8 = 50%.

Multiple choice

Directions: There are two bags. The first bag has 9 red balls and 7 blue balls. The second bag has 8 red balls and 6 blue balls. One ball is drawn from first bag and put in the second bag. Then one ball is drawn from second bag. What is probability that the ball drawn from second bag is blue?

  1. 103 240

  2. 9 16

  3. 7 15

  4. 6 15

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

Bag 1: 9R, 7B. Bag 2: 8R, 6B. Case 1: Red drawn from Bag 1 (9/16). Bag 2 becomes 9R, 6B. P(Blue from Bag 2) = 6/15. Case 2: Blue drawn from Bag 1 (7/16). Bag 2 becomes 8R, 7B. P(Blue from Bag 2) = 7/15. Total P = (9/16 * 6/15) + (7/16 * 7/15) = (54 + 49) / 240 = 103/240.

Multiple choice

A bag contains x green balls, 7 blue balls and 8 red balls. When two balls are drawn from bag randomly, then the probability of one ball being green and one ball being red is 4/15. Find value of x (number of green balls cannot be more than 18 balls).

  1. 3

  2. 5

  3. 10

  4. 9

  5. 15
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total balls = x + 15. Probability of one green and one red is [xC1 * 8C1] / [(x+15)C2] = 4/15. This simplifies to 8x / [((x+15)(x+14))/2] = 4/15, or 16x / (x^2 + 29x + 210) = 4/15. Solving 60x = x^2 + 29x + 210 gives x^2 - 31x + 210 = 0, which factors to (x-10)(x-21) = 0. Given x <= 18, x = 10.