Probability · NDA previous year questions

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2019 25 questions

Q1072019 · 17 Nov 2019
A bag contains 20 books out of which 5 are defective. If 3 of the books are selected at random and removed from the bag in succession without replacement, then what is the probability that all three books are defective?
1. A.0.009
2. B.0.016
3. C.0.026
4. D.0.047
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Answer: A
Q1082019 · 17 Nov 2019
A coin is biased so that heads comes up thrice as likely as tails. For three independent tosses of a coin, what is the probability of getting at most two tails?
1. A.0.16
2. B.0.48
3. C.0.58
4. D.0.98
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Answer: D
Q1092019 · 17 Nov 2019
If a coin is tossed till the first head appears, then what will be the sample space?
1. A.{H}
2. B.{TH}
3. C.{T, HT, HHT, HHHT, ................}
4. D.{H, TH, TTH, TTTH, ................}
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Answer: D
Q1112019 · 17 Nov 2019
If a fair die is rolled 4 times, then what is the probability that there are exactly 2 sixes?
1. A. $\frac{5}{216}$
2. B. $\frac{25}{216}$
3. C. $\frac{125}{216}$
4. D. $\frac{175}{216}$
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Answer: B
Q1122019 · 17 Nov 2019
Consider the following statements : 1. If $A$ and $B$ are mutually exclusive events, then it is possible that $P (A) = P (B) = 0.6$ . 2. If $A$ and $B$ are any two events such that $P (A ∣ B) = 1$ , then $P (\overset{ˉ}{B} ∣ \overset{ˉ}{A}) = 1$ . Which of the above statements is/are correct?
1. A.1 only
2. B.2 only
3. C.Both 1 and 2
4. D.Neither 1 nor 2
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Answer: B
Q1132019 · 17 Nov 2019
There are 3 coins in a box. One is a two-headed coin; another is a fair coin; and third is biased coin that comes up heads 75% of time. When one of the three coins is selected at random and flipped, it shows heads. What is the probability that it was the two-headed coin?
1. A. $\frac{2}{9}$
2. B. $\frac{1}{3}$
3. C. $\frac{4}{9}$
4. D. $\frac{5}{9}$
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Answer: C
Q1142019 · 17 Nov 2019
If 5 of a Company's 10 delivery trucks do not meet emission standards and 3 of them are chosen for inspection, then what is the probability that none of the trucks chosen will meet emission standards?
1. A. $\frac{1}{8}$
2. B. $\frac{3}{8}$
3. C. $\frac{1}{12}$
4. D. $\frac{1}{4}$
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Answer: C
Q1152019 · 17 Nov 2019
Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on them is a prime number?
1. A. $\frac{5}{12}$
2. B. $\frac{1}{2}$
3. C. $\frac{7}{12}$
4. D. $\frac{2}{3}$
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Answer: A
Q1162019 · 17 Nov 2019
What is the value of $2 + \frac{1}{2 + \frac{1}{2 + \frac{1}{2 + \dots \infty}}} ?$
1. A. $2 - 1$
2. B. $2 + 1$
3. C.3
4. D.4
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Answer: B
Q1002019 · 21 Apr 2019
Let the correlation coefficient between X and Y be 0.6. Random variables Z and W are defined as $Z = X + 5$ and $W = \frac{Y}{3}$ . What is the correlation coefficient between Z and W?
1. A.0.1
2. B.0.2
3. C.0.36
4. D.0.6
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Answer: D
Q1032019 · 21 Apr 2019
From a deck of cards, cards are taken out with replacement. What is the probability that the fourteenth card taken out is an ace?
1. A. $\frac{1}{51}$
2. B. $\frac{4}{51}$
3. C. $\frac{1}{52}$
4. D. $\frac{1}{13}$
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Answer: D
Q1042019 · 21 Apr 2019
If A and B are two events such that P(A) = 0.5, P(B) = 0.6 and $P (A \cap B) = 0.4$ , then what is $P (\overline{A \cup B})$ equal to?
1. A.0.9
2. B.0.7
3. C.0.5
4. D.0.3
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Answer: D
Q1052019 · 21 Apr 2019
A problem is given to three students A, B and C whose probabilities of solving the problem are $\frac{1}{2}$ , $\frac{3}{4}$ and $\frac{1}{4}$ respectively. What is the probability that the problem will be solved if they all solve the problem independently?
1. A. $\frac{29}{32}$
2. B. $\frac{27}{32}$
3. C. $\frac{25}{32}$
4. D. $\frac{23}{32}$
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Answer: A
Q1062019 · 21 Apr 2019
A pair of fair dice is rolled. What is the probability that the second dice lands on a higher value than does the first?
1. A. $\frac{1}{4}$
2. B. $\frac{1}{6}$
3. C. $\frac{5}{12}$
4. D. $\frac{5}{18}$
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Answer: C
Q1072019 · 21 Apr 2019
A fair coin is tossed and an unbiased dice is rolled together. What is the probability of getting a 2 or 4 or 6 along with head?
1. A. $\frac{1}{2}$
2. B. $\frac{1}{3}$
3. C. $\frac{1}{4}$
4. D. $\frac{1}{6}$
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Answer: C
Q1082019 · 21 Apr 2019
If A, B, C are three events, then what is the probability that at least two of these events occur together?
1. A. $P (A \cap B) + P (B \cap C) + P (C \cap A)$
2. B. $P (A \cap B) + P (B \cap C) + P (C \cap A) - P (A \cap B \cap C)$
3. C. $P (A \cap B) + P (B \cap C) + P (C \cap A) - 2 P (A \cap B \cap C)$
4. D. $P (A \cap B) + P (B \cap C) + P (C \cap A) - 3 P (A \cap B \cap C)$
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Answer: C
Q1092019 · 21 Apr 2019
Two independent events A and B are such that $P (A \cup B) = \frac{2}{3}$ and $P (A \cap B) = \frac{1}{6}$ . If $P (B) < P (A)$ , then what is P(B) equal to?
1. A. $\frac{1}{4}$
2. B. $\frac{1}{3}$
3. C. $\frac{1}{2}$
4. D. $\frac{1}{6}$
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Answer: B
Q1102019 · 21 Apr 2019
If two fair dice are rolled then what is the conditional probability that the first dice lands on 6 given that the sum of numbers on the dice is 8?
1. A. $\frac{1}{3}$
2. B. $\frac{1}{4}$
3. C. $\frac{1}{5}$
4. D. $\frac{1}{6}$
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Answer: C
Q1112019 · 21 Apr 2019
Two symmetric dice flipped with each dice having two sides painted red, two painted black, one painted yellow and the other painted white. What is the probability that both land on the same colour?
1. A. $\frac{3}{18}$
2. B. $\frac{2}{9}$
3. C. $\frac{5}{18}$
4. D. $\frac{1}{3}$
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Answer: C
Q1122019 · 21 Apr 2019
There are $n$ socks in a drawer, of which 3 socks are red. If 2 of the socks are chosen randomly and the probability that both selected socks are red is $\frac{1}{2}$ , then what is the value of $n$ ?
1. A.3
2. B.4
3. C.5
4. D.6
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Answer: B
Q1132019 · 21 Apr 2019
Two cards are chosen at random from a deck of 52 playing cards. What is the probability that both of them have the same value?
1. A. $\frac{1}{17}$
2. B. $\frac{3}{17}$
3. C. $\frac{5}{17}$
4. D. $\frac{7}{17}$
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Answer: A
Q1142019 · 21 Apr 2019
In eight throws of a die, 5 or 6 is considered a success. The mean and standard deviation of total number of successes is respectively given by
1. A. $\frac{8}{3}, \frac{16}{9}$
2. B. $\frac{8}{3}, \frac{4}{3}$
3. C. $\frac{4}{3}, \frac{4}{3}$
4. D. $\frac{4}{3}, \frac{16}{9}$
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Answer: B
Q1152019 · 21 Apr 2019
A and B are two events such that $\overline{A}$ and $\overline{B}$ are mutually exclusive. If P(A) = 0.5 and P(B) = 0.6, then what is the value of $P (A ∣ B)$ ?
1. A. $\frac{1}{5}$
2. B. $\frac{1}{6}$
3. C. $\frac{2}{5}$
4. D. $\frac{1}{3}$
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Answer: B
Q1162019 · 21 Apr 2019
What is the probability that an interior point in a circle is closer to the centre than to the circumference?
1. A. $\frac{1}{4}$
2. B. $\frac{1}{2}$
3. C. $\frac{3}{4}$
4. D.It cannot be determined
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Answer: A
Q1172019 · 21 Apr 2019
If A and B are two events, then what is the probability of occurrence of either event A or event B?
1. A. $P (A) + P (B)$
2. B. $P (A \cup B)$
3. C. $P (A \cap B)$
4. D. $P (A) P (B)$
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Answer: B