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

One week before New Year, Joy sent $8$ greeting cards to his friends in Delhi and $12$ to his friends in Mumbai. If a card is picked randomly from the cards that were sent by him, what is the probability of picking a card which is not for a friend in Delhi?
  1. $\dfrac {8}{25}$
  2. $\dfrac {12}{25}$
  3. $\dfrac {3}{5}$
  4. $\dfrac {4}{5}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total cards = 8 + 12 = 20. Cards not for Delhi are the ones for Mumbai = 12. Probability = 12 / 20 = 3 / 5.

Multiple choice

A ball is drawn from a box containing $6$ red balls, $4$ blue and $5$ green. Calculate What is the probability that the ball will be red or white?
  1. $\dfrac{10}{15}$
  2. $\dfrac{11}{15}$
  3. $\dfrac{9}{15}$

  4. none of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total balls = 6 + 4 + 5 = 15. Probability of red = 6/15. Probability of white = 0/15 (no white balls mentioned). Probability of red or white = 6/15 = 2/5. Since 2/5 is not listed, 'none of these' is correct.

Multiple choice

Obtain the sample space of an experiment that consists of a fair coin being tossed four times. Consider the following events: A is the event all four results are the same. B is the event exactly one Head occurs. C is the event at least two Heads occur. Calculate p(A)?
  1. $\dfrac{1}{16}$
  2. $\dfrac{2}{16}$
  3. $\dfrac{3}{16}$
  4. $\dfrac{5}{16}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total outcomes for 4 coin tosses = 2^4 = 16. Event A (all same) is {HHHH, TTTT}, so 2 outcomes. P(A) = 2/16.

Multiple choice

A random sample of $1,000$ men was selected and each individual was asked to indicate his age and his favorite sport. The results were as follows. Age/ Sports Volleyball Basket ball Hockey Football Below $20$ $26$ $47$ $41$ $36$ $20-29$ $38$ $84$ $80$ $48$ $30-39$ $72$ $68$ $38$ $22$ $40-49$ $96$ $48$ $30$ $26$ $50$ and above $134$ $44$ $18$ $4$ If a respondent is selected at random, what is the probability that he doesn't prefer Hockey
  1. $\dfrac {793}{1000}$
  2. $\dfrac {93}{1000}$
  3. $\dfrac {73}{1000}$

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

Total respondents = 1000. Total who prefer Hockey: 41 + 80 + 38 + 30 + 18 = 207. Probability of preferring Hockey = 207/1000. Probability of NOT preferring Hockey = 1 - 207/1000 = 793/1000.

Multiple choice

Three dice are thrown simultaneously. Find the probability of getting the same number on all the three dice.
  1. $\dfrac{1}{36}$  
  2. $\dfrac{1}{3}$  
  3. $\dfrac{5}{36}$  

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

When three dice are thrown, there are 6*6*6 = 216 total outcomes. The outcomes where all three dice show the same number are (1,1,1), (2,2,2), (3,3,3), (4,4,4), (5,5,5), and (6,6,6), which is 6 outcomes. Probability = 6/216 = 1/36.

Multiple choice

Two dice are rolled simultaneously. Find the probability that the sum of the numbers on the faces is neither divisible by 3 nor by 4.
  1. $\dfrac{4}{7}$
  2. $\dfrac{4}{9}$
  3. $\dfrac{2}{9}$

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

Total outcomes = 36. Sums divisible by 3: 3, 6, 9, 12 (counts: 2, 5, 4, 1 = 12). Sums divisible by 4: 4, 8, 12 (counts: 3, 5, 1 = 9). Sums divisible by both 3 and 4 (i.e., 12): 1. Union = 12 + 9 - 1 = 20. Neither divisible = 36 - 20 = 16. Probability = 16/36 = 4/9.