Quantitative Aptitude
Probability
1,860 Questions
Probability Questions
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$\dfrac{1}{5}$
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$\dfrac{2}{5}$
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$\dfrac{3}{5}$
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$\dfrac{1}{2}$
B
Correct answer
Explanation
The probability of choosing red from box A is 3/5, and from box B it is 2/10 = 1/5. Since each box is selected with probability 1/2, the total probability is (1/2)(3/5) + (1/2)(1/5) = 2/5.
A
Correct answer
Explanation
Total balls = (12x + 3) + (5x + 1) = 17x + 4. Probability of 2 red balls = [(12x+3)/(17x+4)] * [(12x+2)/(17x+3)] = 1/2. Testing x=1 gives 15 red, 6 black, total 21. Probability = (15/21) * (14/20) = (5/7) * (7/10) = 35/70 = 1/2. Thus, total balls = 21.
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$81/625$
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$27/125$
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$81/125$
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$27/625$
A
Correct answer
Explanation
Total balls = 15. Non-red balls = 4+5 = 9. Probability of drawing a non-red ball = 9/15 = 3/5. Since it is with replacement, the probability of drawing 4 non-red balls is (3/5)^4 = 81/625.
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$1:\;31\;$
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$31\;:\;1\;$
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$31:\;32\;$
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$1:\;32$
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$\dfrac {11}{30}$
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$\dfrac {23}{30}$
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$\dfrac {26}{30}$
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$\dfrac {1}{10}$
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$1:4, 1:13$
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$1:3, 1:12$
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$1:6, 1:12$
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$1:8, 1:26$
B
Correct answer
Explanation
There are 13 spades in a 52-card deck, so the odds in favor are 13:39, which simplifies to 1:3. There are 4 kings, so the odds in favor are 4:48, which simplifies to 1:12.
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$\cfrac{3}{5}$
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$\cfrac{2}{15}$
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$\cfrac{1}{2}$
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$\cfrac{1}{3}$
C
Correct answer
Explanation
For any number of tosses n, the probability of getting an odd number of tails is 1/2, because the binomial expansion of (p+q)^n and (p-q)^n shows that the sum of odd-indexed terms equals the sum of even-indexed terms when p=q=1/2.
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$\cfrac{4}{5}$
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$\cfrac{7}{16}$
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$\cfrac{3}{16}$
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$\cfrac{3}{20}$
C
Correct answer
Explanation
Probability of odd number (success) p = 1/2. n = 5. P(X >= 4) = P(X=4) + P(X=5). P(X=4) = 5C4 * (1/2)^5 = 5/32. P(X=5) = 5C5 * (1/2)^5 = 1/32. Total = 6/32 = 3/16.
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$30:6$
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$29:7$
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$5:31$
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$31:5$
C
Correct answer
Explanation
Total outcomes when throwing two dice = 36. Sum of 6 can be (1,5), (2,4), (3,3), (4,2), (5,1) = 5 outcomes. Odds in favour = (Number of favorable outcomes) : (Number of unfavorable outcomes) = 5 : (36 - 5) = 5 : 31.
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$\cfrac{2}{3}$
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$\cfrac{3}{4}$
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$\cfrac{5}{12}$
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none of these
A
Correct answer
Explanation
The odd numbers on a die are {1, 3, 5}. Among these, only {3, 5} are prime numbers. Thus, the probability is 2/3.
A
Correct answer
Explanation
Face cards are Jack, Queen, King in each of 4 suits, total 12. Probability of A = 12/52 = 3/13. Odds in favor = P(A) / (1 - P(A)) = (3/13) / (10/13) = 3/10.
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$\displaystyle \frac {1}{9}$
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$ \dfrac {1}{3}$
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$ \dfrac {2}{3}$
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$ \dfrac {2}{9}$
A
Correct answer
Explanation
Let p1, p2 be probabilities. p1 = p2^2. Odds against 1 = (1-p1)/p1. Odds against 2 = (1-p2)/p2. (1-p1)/p1 = ((1-p2)/p2)^3. Substituting p1 = p2^2: (1-p2^2)/p2^2 = (1-p2)^3/p2^3. (1-p2)(1+p2)/p2^2 = (1-p2)^3/p2^3. (1+p2)/1 = (1-p2)^2/p2. p2^2 + p2 = 1 - 2p2 + p2^2. 3p2 = 1, p2 = 1/3. p1 = (1/3)^2 = 1/9.
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$3:5$
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$2:5$
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$3:2$
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None of these
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$\dfrac {2}{3}, .666$ or $.667$
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$\dfrac {2}{4}$
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$\dfrac {3}{4}$
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$\dfrac {1}{3}$
A
Correct answer
Explanation
Total vegetables = 15 + 20 + 25 = 60. Carrots = 20. Not carrots = 60 - 20 = 40. Probability = 40/60 = 2/3.
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$\dfrac {1}{2}$
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$\dfrac {2}{3}$
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$\dfrac {3}{4}$
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$\dfrac {7}{12}$
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$\dfrac {7}{36}$
B
Correct answer
Explanation
Total socks = 7 + 12 + 17 = 36. The number of non-white socks is 7 (black) + 17 (red) = 24. The probability is 24/36, which simplifies to 2/3.