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 box contains $40$ red and blue marbles. If a marble is drawn at random, the probability of picking a blue marble is $\dfrac {3}{8}$. Ansh takes out one red and nine blue marbles and then draws a marble at random. Find the probability of drawing a blue marble
  1. $\dfrac {4}{5}$
  2. $\dfrac {2}{5}$
  3. $\dfrac {7}{40}$
  4. $\dfrac {1}{5}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total marbles = 40. Blue = (3/8)*40 = 15. Red = 25. After removing 1 red and 9 blue: Total = 40 - 10 = 30. Blue = 15 - 9 = 6. Probability = 6/30 = 1/5.

Multiple choice

Two coins are tossed $1000$ times and the outcomes are recorded as below: No of heads $2$ $1$ $0$ Frequency $200$ $550$ $250$ Based on this information, the probability for at most one head is $\dfrac{a}{b}$. Where $(a,b)=1$, then
  1. $\dfrac{1}{5}$
  2. $\dfrac{1}{4}$
  3. $\dfrac{4}{5}$
  4. $\dfrac{3}{4}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total tosses = 1000. At most one head means 0 or 1 head. Frequency of 0 heads = 250, frequency of 1 head = 550. Total favorable = 250 + 550 = 800. Probability = 800 / 1000 = 4/5.

Multiple choice

A die is thrown $400$ times, the frequency of the outcomes of the events are given as under. outcome $1$ $2$ $3$ $4$ $5$ $6$ Frequency $70$ $65$ $60$ $75$ $63$ $67$ Find the probability of occurrence of an odd number.
  1. The probability of occurrence of odd number$=\dfrac{5}{7}$
  2. The probability of occurrence of odd number$=\dfrac{9}{2}$
  3. The probability of occurrence of odd number$=\dfrac{193}{400}$
  4. The probability of occurrence of odd number$=\dfrac{200}{299}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Odd outcomes are 1, 3, and 5. Frequencies are 70, 60, and 63. Total odd frequency = 70 + 60 + 63 = 193. Total trials = 400. Probability = 193/400.

Multiple choice

Two balls are drawn at random with replacement from a box containing $10$ black and $8$ red balls. Find the probability that (i) both balls are red. (ii) first ball is black and second is red. (iii) one of them is black and other is red.
  1. $0.56,\ 0.75,\ 0.67$
  2. $0.46,\ 0.56,\ 0.36$
  3. $0.56,\ 0.76,\ 0.76$
  4. $0.19,\ 0.24,\ 0.49$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total balls = 18. P(Black) = 10/18 = 5/9, P(Red) = 8/18 = 4/9. (i) Both Red: (4/9)(4/9) = 16/81 approx 0.197. (ii) Black then Red: (5/9)(4/9) = 20/81 approx 0.247. (iii) One Black, one Red: (5/9)(4/9) + (4/9)(5/9) = 40/81 approx 0.494. Option D matches these values.

Multiple choice

$5$ coins tossed whose marks $2$ and $3$,then the probability of total sum $12$ is :
  1. $\dfrac{1}{{32}}$
  2. $\dfrac{1}{{16}}$
  3. $\dfrac{3}{{16}}$
  4. $\dfrac{5}{{16}}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

With 5 coins having faces 2 and 3, the total sum can range from 10 to 15. The number of ways to get a sum of 12 is equivalent to choosing how many coins show 3. If x coins show 3 and (5-x) coins show 2, 3x + 2(5-x) = 12, so x + 10 = 12, x = 2. The number of ways to choose 2 coins out of 5 is 5C2 = 10. Total outcomes are 2^5 = 32. Probability = 10/32 = 5/16.

Multiple choice

A six- faced dice is so biased that it is twice as likely to show an even number as an odd number when thrown. it is thrown twice. The probability that the sum of two numbers thrown is even is :
  1. $1/12$
  2. $1/6$
  3. $1/3$
  4. $5/9$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The probability of an even result is twice the probability of an odd result, so P(even) = 2/3 and P(odd) = 1/3. An even sum occurs when both results have the same parity, giving (2/3)^2 + (1/3)^2 = 5/9.