Aptitude Questions on Probability for
Q. Inside a bag, there are 5 red balls, 4 blue balls, and 3 green balls. If you were to reach into the bag, eyes closed, and pick just one ball, what is the chance that the ball you grab is either red or green?
A) $( \frac{5}{12} ) $
B) $( \frac{3}{12} ) $
C) $( \frac{8}{12} ) $
D) $( \frac{7}{12} )$
Check Solution
Ans: C) $( \frac{8}{12} )$
Total balls = ( 5 + 4 + 3 = 12 ).
Favorable outcomes (red or green) = ( 5 + 3 = 8 ).
Probability = $( \frac{8}{12} = \frac{2}{3} )$.
Q. 2 You’re at a game night rolling two standard six-sided dice. You’re feeling lucky and decide to bet on the total sum of the dice being exactly 8. What are the odds that your roll will make you a winner?
A) $( \frac{5}{36} ) $
B) $( \frac{6}{36} ) $
C) $( \frac{7}{36} )$
D) $( \frac{4}{36} )$
Check Solution
Ans: A) $( \frac{5}{36} )$
Possible outcomes for a sum of 8 are ( (2,6), (3,5), (4,4), (5,3), (6,2) ).
Number of favorable outcomes = 5.
Total outcomes = $( 6 \times 6 = 36 )$.
Probability = $( \frac{5}{36} )$.
Q. 3 You’re holding a freshly shuffled deck of 52 cards, ready for some card magic. With a dramatic flair, you draw a single card. What’s the probability that your card is either a queen or a diamond from the deck?
A) $( \frac{17}{52} ) $
B) $( \frac{4}{13} )$
C) $( \frac{16}{52} )$
D) $( \frac{15}{52} )$
Check Solution
Ans: B) $( \frac{4}{13} )$
There are 4 queens and 13 diamonds in the deck.
One queen is also a diamond.
Favorable outcomes = ( 4 + 13 – 1 = 16 ).
Probability = $( \frac{16}{52} = \frac{4}{13} )$.
Q. 4 Imagine flipping a shiny, fair coin twice, hoping to see at least one head appear. What’s the probability that your coin tosses will deliver at least one head?
A) $( \frac{3}{4} )$
B) $( \frac{1}{4} )$
C) $( \frac{1}{2} )$
D) $( \frac{7}{8} )$
Check Solution
Ans: A) $( \frac{3}{4} )$
Probability of no head (both tails) = $( \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} )$.
Probability of at least one head = $( 1 – \frac{1}{4} = \frac{3}{4} )$.
Q. 5 In a box of 10 light bulbs, 3 of them have unfortunately turned out defective. If you randomly select 2 bulbs from the box without peeking, what’s the likelihood that both bulbs you pick are the faulty ones?
A) $( \frac{1}{15} )$
B) $( \frac{1}{30} )$
C) $( \frac{1}{10} )$
D) $( \frac{1}{20} )$
Check Solution
Ans: A) $( \frac{1}{15} )$
Total ways to choose 2 bulbs = $( \binom{10}{2} = 45 )$.
Ways to choose 2 defective bulbs = $( \binom{3}{2} = 3 )$.
Probability = $( \frac{3}{45} = \frac{1}{15} )$.
Q. 6 You’re tasked with forming a committee of 3 members from a pool of 5 men and 3 women. To ensure diversity, you want at least one woman on the committee. What’s the probability that your committee will include at least one woman?
A) $( \frac{35}{56} )$
B) $( \frac{21}{56} $
C) $( \frac{41}{56} $
D) $( \frac{47}{56} )$
Check Solution
Ans: C) $( \frac{41}{56} )$
Total ways = $( \binom{8}{3} = 56 )$.
Ways to select only men = $( \binom{5}{3} = 10 )$.
Ways with at least one woman = $( 56 – 10 = 46 )$.
Probability = $( \frac{46}{56} = \frac{41}{56} )$.
Q. 7 You toss three fair coins into the air, watching them spin and fall with a mix of anticipation and excitement. What is the probability that exactly two of those coins land showing heads?
A) $( \frac{1}{8} )$
B) $( \frac{3}{8} )$
C) $( \frac{1}{4} )$
D) $( \frac{1}{2} )$
Check Solution
Ans: B) $( \frac{3}{8} )$
Total outcomes = $( 2^3 = 8 )$.
Favorable outcomes = $( { HHT, HTH, THH } = 3 )$.
Probability = $( \frac{3}{8} )$.
Q. 8 A street cricket team of 3 is to be formed from 5 batsmen and 3 bowlers. You are hoping to see at least one bowler in the team, who can take some wickets. What is the probability that your wish will come true?
A) $\frac{35}{56}$
B) $\frac{21}{56}$
C) $\frac{41}{56}$
D) $\frac{47}{56}$
Check Solution
Ans: C) $\frac{41}{56}$
Total ways = $\binom{8}{3} = 56$
Ways to select only men = $\binom{5}{3} = 10$
Ways with at least one woman = $56−10=46$
Probability = $\frac{46}{56} = \frac{41}{56}$
Q. 9 The probability of rain in Surat is calculated as $\frac{2}{5}$ by weather department for tomorrow, what is the probability that it doesn’t rain in Surat tomorrow?
A) $\frac{1}{5}$
B) $\frac{3}{5}$
C) $\frac{4}{5}$
D) $\frac{2}{5}$
Check Solution
Ans: B) $\frac{3}{5}$
Probability of not happening = $1 – \frac{2}{5} = \frac{3}{5}$
Q. 10 A bag contains 4 white and 5 black balls. If you randomly draw two balls without looking, what is the probability that both of the balls you select turn out to be black?
A) $\frac{2}{9}$
B) $\frac{1}{3}$
C) $\frac{5}{18}$
D) $\frac{10}{36}$
Check Solution
Ans: C) $\frac{5}{18}$
Total ways to choose 2 balls = $\binom{9}{2} = 36$
Ways to choose 2 black balls = $\binom{5}{2} = 10$
Probability = $\frac{10}{36} = \frac{5}{18}$
Refer Questions for next topic: https://www.learntheta.com/aptitude-questions-geometry/