Quantitative Aptitude
Probability
1,860 Questions
Probability Questions
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$0$
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$\dfrac{1}{2}$
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$1$
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$2$
B
Correct answer
Explanation
An unbiased coin has two equally likely outcomes: head or tail. The probability of getting a head is the number of favorable outcomes divided by the total number of outcomes, which is 1/2.
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$\dfrac{1}{3}$
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$\dfrac{2}{3}$
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$\dfrac{1}{2}$
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$\dfrac{1}{8}$
B
Correct answer
Explanation
The odd numbers on a die are 1, 3, and 5. Among these, 3 and 5 are prime numbers. Therefore, the probability is 2/3.
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$\displaystyle \frac{11}{36}$
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$\displaystyle \frac{25}{36}$
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$\displaystyle \frac{1}{6}$
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$\displaystyle \frac{1}{8}$
A
Correct answer
Explanation
Probability of not getting a 1 on one die is 5/6. Probability of not getting a 1 on two dice is (5/6)^2 = 25/36. Probability of at least one 1 is 1 - 25/36 = 11/36.
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$\displaystyle \frac{1}{26}$
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$\displaystyle \frac{1}{221}$
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$\displaystyle \frac{1}{2}$
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None of these.
B
Correct answer
Explanation
The probability of drawing two aces is (4/52) * (3/51) = (1/13) * (1/17) = 1/221.
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$\dfrac{5}{7}$
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$\dfrac{1}{7}$
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$\dfrac{7}{15}$
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$\dfrac{1}{15}$
C
Correct answer
Explanation
Total balls = 6. Ways to choose 2 balls = 6C2 = 15. Ways to choose 2 white = 4C2 = 6. Ways to choose 2 black = 2C2 = 1. Total favorable = 6 + 1 = 7. Probability = 7/15.
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$\dfrac{19}{144}$
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$\dfrac{25}{216}$
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$\dfrac{125}{216}$
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$\dfrac{175}{216}$
A
Correct answer
Explanation
Probability of at least 2 sixes = 1 - P(0 sixes) - P(1 six). P(0) = (5/6)^4 = 625/1296. P(1) = 4 * (1/6) * (5/6)^3 = 500/1296. Result = 1 - 1125/1296 = 171/1296 = 19/144.
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$13/4$
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$4/13$
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$1/52$
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$52$.
C
Correct answer
Explanation
Probability of drawing a diamond is 13/52 = 1/4. Probability of drawing a king is 4/52 = 1/13. Since the first is replaced, the events are independent. Probability = (1/4) * (1/13) = 1/52.
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$\displaystyle \frac{1}{36}$
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$\displaystyle \frac{5}{36}$
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$\displaystyle \frac{25}{36}$
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$\displaystyle \frac{1}{6}$
B
Correct answer
Explanation
The required event is an ace on the first throw and not an ace on the second throw. Its probability is 1/6 × 5/6 = 5/36, so option B is correct.
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$\dfrac{1}{2}$
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$\dfrac{1}{3}$
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$\dfrac{1}{4}$
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$\dfrac{1}{8}$
C
Correct answer
Explanation
Each die has 3 odd numbers (1, 3, 5) out of 6. Probability of one die being odd is 3/6 = 1/2. Probability for both is (1/2) * (1/2) = 1/4.
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$\dfrac{1}{4}$
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$\dfrac{1}{3}$
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$\dfrac{1}{2}$
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$\dfrac{1}{8}$
C
Correct answer
Explanation
Total outcomes for 3 coin tosses is 2^3 = 8. Outcomes with at least two heads are HHH, HHT, HTH, THH. There are 4 such outcomes. Probability = 4 / 8 = 1/2.
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$\displaystyle \frac{1}{4}$
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$\displaystyle \frac{3}{8}$
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$\displaystyle \frac{1}{2}$
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$\displaystyle \frac{1}{6}$
C
Correct answer
Explanation
Tossing three coins yields 2^3 = 8 outcomes. Outcomes with at least two heads are HHH, HHT, HTH, THH, which is 4 outcomes. Probability = 4/8 = 1/2.
D
Correct answer
Explanation
Total outcomes = 36. Sum of 10: (4,6), (5,5), (6,4). Probability = 3/36 = 1/12.
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$\displaystyle \frac{1}{2}$
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$\displaystyle \frac{2}{3}$
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$\displaystyle \frac{1}{3}$
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$\displaystyle \frac{1}{4}$
D
Correct answer
Explanation
When tossing two coins, the sample space is {HH, HT, TH, TT}. There is only one outcome with two heads, so the probability is 1/4.
B
Correct answer
Explanation
Let w be the number of white balls. Total balls = 5 + w. P(white) = w / (5 + w). P(yellow) = 5 / (5 + w). Given P(white) = 2 * P(yellow), so w / (5 + w) = 2 * (5 / (5 + w)). Thus w = 10.
C
Correct answer
Explanation
Total balls = 6 + 4 + 8 = 18. White balls = 8. Not white balls = 18 - 8 = 10. Probability = 10 / 18 = 5/9.