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

A bag consists of 100 shirts of which 88 are good, 8 have minor defects and 4 have major defects. A trader A will accept only the shirt which are good, but the trader B will not accept the shirts which have major defects. One shirt is drawn at random. What is the probability that it is acceptable by (i) A (ii) B ?
  1. (i) $\dfrac{21}{25}$    (ii) $\dfrac{23}{25}$ 
  2. (i) $\dfrac{22}{25}$    (ii) $\dfrac{24}{25}$ 
  3. (i) $\dfrac{11}{25}$    (ii) $\dfrac{13}{25}$ 

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

Total shirts = 100. Good = 88, Minor = 8, Major = 4. Trader A accepts only good (88/100 = 22/25). Trader B accepts all except major (100 - 4 = 96/100 = 24/25).

Multiple choice

Piggybank contains $100$ fifty-paise coins, $50$ one-rupee coins, $20$ two-rupees coins and $10$ five- rupees coins. One coin is drawn at random. Find the probability that the drawn coin (i) will be a fifty-paise coin (ii) will not be a five-rupees coin.
  1. (i) $\dfrac{4}{9}$    (ii) $\dfrac{17}{18}$ 
  2. (i) $\dfrac{5}{9}$    (ii) $\dfrac{17}{18}$ 
  3. (i) $\dfrac{5}{9}$    (ii) $\dfrac{14}{18}$ 

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

Total coins = 100 + 50 + 20 + 10 = 180. (i) P(fifty-paise) = 100/180 = 5/9. (ii) P(not five-rupees) = 1 - P(five-rupees) = 1 - 10/180 = 1 - 1/18 = 17/18.

Multiple choice

Two dice are rolled and the product of the outcomes (numbers) are found. What is the probability that the product so found is a prime number?
  1. $\dfrac{1}{7}$  
  2. $\dfrac{1}{6}$  
  3. $\dfrac{5}{6}$  

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

There are 36 possible outcomes when rolling two dice. The products that are prime numbers are (1,2), (2,1), (1,3), (3,1), (1,5), and (5,1). There are 6 such outcomes, so the probability is 6/36 = 1/6.

Multiple choice

A box contains $5$ red and $4$ white marbles. Two marbles are drawn successively from the box without replacement and the second drawn marble drawn is found to be white. Probability that the first marble is also while is?
  1. $\displaystyle\frac{3}{8}$
  2. $\displaystyle\frac{1}{2}$
  3. $\displaystyle\frac{1}{3}$
  4. $\displaystyle\frac{1}{4}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given that the second marble is white, there are 8 possible remaining first-marble positions in the conditional sample space, of which 3 correspond to a white first marble. Thus, the probability is 3/8.

Multiple choice

A bag contains 10 white and 15 black balls. Two balls are drawn without replacement find the probability that first is black and second is white......
  1. $\dfrac{1}{7}$
  2. $\dfrac{1}{4}$
  3. $\dfrac{1}{8}$
  4. $\dfrac{1}{5}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total balls = 25. P(first is black) = 15/25 = 3/5. After removing one black ball, 24 balls remain (10 white, 14 black). P(second is white | first is black) = 10/24 = 5/12. Probability = (3/5) * (5/12) = 15/60 = 1/4.