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

What is the probability that the first $2$ draws from a pack of cards are clubs and the third is a spade? (Assume all cards are drawn without replacement)
  1. $\cfrac { 2,028 }{ 132,600 } $
  2. $\cfrac { 38 }{ 132,600 } $
  3. $\cfrac { 1,716}{ 132,600 } $
  4. $\cfrac { 2,028 }{ 140,608 } $
  5. $\cfrac { 1,716 }{ 140,608 } $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

There are 52 cards. The probability of drawing a club is 13/52. Without replacement, the probability of the second being a club is 12/51. The probability of the third being a spade is 13/50. Multiplying these: (13/52) * (12/51) * (13/50) = (1/4) * (4/17) * (13/50) = 13 / (17 * 50) = 13 / 850. Converting to the denominator 132600: (13 * 156) / (850 * 156) = 2028 / 132600.

Multiple choice

A bag contains 12 balls out of which x balls are white. (i) If one ball is drawn at random, what is the probability that it will be a white ball. (ii) If 6 more white balls are put in the bag and if the probability of drawing a white ball will be twice that of in (i), then find x.
  1. (i) $\dfrac{1}{4}$    (ii) $3$ 
  2. (i) $\dfrac{1}{3}$    (ii) $3$ 
  3. (i) $\dfrac{1}{5}$    (ii) $3$ 

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

For (i), the probability is x/12. For (ii), the new number of white balls is x + 6 and total balls is 18. The probability is (x + 6)/18. Given (x + 6)/18 = 2 * (x/12), we get (x + 6)/18 = x/6, so x + 6 = 3x, 2x = 6, x = 3. The probability in (i) is 3/12 = 1/4.

Multiple choice

A coin is tossed $400$ times and the data of outcomes is below: Outcomes $H$ $T$ Frequency $280$ $120$ Find: (i) $P(H)$, i.e., probability of getting head (ii) $P (T)$, i.e., probability of getting tail. (iii) The value of $P (H) + P (T)$.
  1. $(i)\, 0.5$
    $(ii)\, 0.2$ 
    $(iii)\, 1$
  2. $(i)\, 0.7$ 
    $(ii)\, 0.3$ 
    $(iii)\, 1$
  3. $(i)\, 0.9$ 
    $(ii)\, 0.4$ 
    $(iii)\, 1$

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

P(H) = 280/400 = 0.7. P(T) = 120/400 = 0.3. P(H) + P(T) = 0.7 + 0.3 = 1.