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

An urn contains $6$ white and $4$ blacks balls. A fair die is rolled and that no.of balls are chosen from the urn. The probability that the balls selected are white is
  1. $\dfrac{1}{2}$
  2. $\dfrac{1}{3}$
  3. $\dfrac{3}{5}$
  4. $\dfrac{1}{6}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total balls = 10 (6W, 4B). Die roll outcomes: 1, 2, 3, 4, 5, 6. If die is k, we choose k balls. Probability of all white = (6Ck / 10Ck) * (1/6). Summing for k=1 to 6: (1/6) * [(6/10) + (15/45) + (20/120) + (15/210) + (6/252) + (1/210)] = 1/2.

Multiple choice

A pack of cards is counted with face downwards. It is found that one card is missing. One card is drawn and is found to be red. Then the ability that the missing card is red.
  1. $\dfrac{25}{51}$
  2. $\dfrac{26}{51}$
  3. $\dfrac{1}{2}$
  4. $\dfrac{25}{52}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If the missing card is red, the probability of drawing a red card is 25/51; if it is black, that probability is 26/51. Applying conditional probability gives the probability that the missing card was red as 25/51.

Multiple choice

A pair of dice are thrown, if 5 appears on atleast one of the dice, then the probability that the sum is 10 or greater, is
  1. $\dfrac { 11 }{ 36 } $
  2. $\dfrac { 2 }{ 9 } $
  3. $\dfrac { 3 }{ 11 } $
  4. $\dfrac { 1 }{ 12 } $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Sample space where 5 appears on at least one die: (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (1,5), (2,5), (3,5), (4,5), (6,5). Total = 11 outcomes. Sum >= 10: (5,5), (5,6), (6,5). Total = 3 outcomes. Probability = 3/11.

Multiple choice

A die is loaded in such a way that each odd number is twice as likely to occur as each even number . Find P(G), where G is the event that a number greater than 3 occurs on a single roll of the die.
  1. $\dfrac{5}{9}$
  2. $\dfrac{4}{9}$
  3. $\dfrac{2}{9}$

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

Let p(even) = x, then p(odd) = 2x. Total probability: 3*x + 3*2x = 1, so 9x = 1, x = 1/9. Odds are 2/9, evens are 1/9. P(G) = P(4) + P(5) + P(6) = 1/9 + 2/9 + 1/9 = 4/9.

Multiple choice

Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is less than seven?
  1. $\dfrac 5{12}$
  2. $\dfrac 7{12}$
  3. $\dfrac 1{12}$

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

There are 36 total outcomes when rolling two dice. The sums less than seven are 2 (1,1), 3 (1,2; 2,1), 4 (1,3; 3,1; 2,2), 5 (1,4; 4,1; 2,3; 3,2), and 6 (1,5; 5,1; 2,4; 4,2; 3,3), totaling 15 outcomes. The probability is 15/36, which simplifies to 5/12.