Probability · NDA previous year questions

353 questions asked across 18 exam years, newest first

Year-wise papers Topic-wise questions

Practise this topic

2018 19 questions

Q1032018 · 9 Sept 2018
If two dice are thrown and at least one of the dice shows 5, then the probability that the sum is 10 or more is
1. A. $\frac{1}{6}$
2. B. $\frac{4}{11}$
3. C. $\frac{3}{11}$
4. D. $\frac{2}{11}$
Show answer
Answer: C
Q1042018 · 9 Sept 2018
Let A, B and C be three mutually exclusive and exhaustive events associated with a random experiment. If $P (B) = 1.5 P (A)$ and $P (C) = 0.5 P (B)$ , then $P (A)$ is equal to
1. A. $\frac{3}{4}$
2. B. $\frac{4}{13}$
3. C. $\frac{2}{3}$
4. D. $\frac{1}{2}$
Show answer
Answer: B
Q1052018 · 9 Sept 2018
In a bolt factory, machines X, Y, Z manufacture bolts that are respectively 25%, 35% and 40% of the factory's total output. The machines X, Y, Z respectively produce 2%, 4% and 5% defective bolts. A bolt is drawn at random from the product and is found to be defective. What is the probability that it was manufactured by machine X?
1. A. $\frac{5}{39}$
2. B. $\frac{14}{39}$
3. C. $\frac{20}{39}$
4. D. $\frac{34}{39}$
Show answer
Answer: A
Q1062018 · 9 Sept 2018
8 coins are tossed simultaneously. The probability of getting at least 6 heads is
1. A. $\frac{7}{64}$
2. B. $\frac{57}{64}$
3. C. $\frac{37}{256}$
4. D. $\frac{229}{256}$
Show answer
Answer: C
Q1072018 · 9 Sept 2018
Three groups of children contain 3 girls and 1 boy; 2 girls and 2 boys; 1 girl and 3 boys. One child is selected at random from each group. The probability that the three selected consist of 1 girl and 2 boys is
1. A. $\frac{13}{32}$
2. B. $\frac{9}{32}$
3. C. $\frac{3}{32}$
4. D. $\frac{1}{32}$
Show answer
Answer: A
Q1082018 · 9 Sept 2018
If the probability of simultaneous occurrence of two events A and B is p and the probability that exactly one of A, B occurs is q, then which of the following is/are correct? 1. $P (\overset{ˉ}{A}) + P (\overset{ˉ}{B}) = 2 - 2 p - q$ 2. $P (\overset{ˉ}{A} \cap \overset{ˉ}{B}) = 1 - p - q$ Select the correct answer using the code given below:
1. A.1 only
2. B.2 only
3. C.Both 1 and 2
4. D.Neither 1 nor 2
Show answer
Answer: C
Q1092018 · 9 Sept 2018
Two integers x and y are chosen with replacement from the set ${0, 1, 2, \dots, 10}$ . The probability that $∣ x - y ∣ > 5$ is
1. A. $\frac{6}{11}$
2. B. $\frac{35}{121}$
3. C. $\frac{30}{121}$
4. D. $\frac{25}{121}$
Show answer
Answer: C
Q1102018 · 9 Sept 2018
Three dice having digits 1, 2, 3, 4, 5 and 6 on their faces are marked I, II and III and rolled. Let x, y and z represent the number on die-I, die-II and die-III respectively. What is the number of possible outcomes such that $x > y > z$ ?
1. A.14
2. B.16
3. C.18
4. D.20
Show answer
Answer: D
Q1112018 · 9 Sept 2018
Consider the following expressions: 1. $x + x^{2} - \frac{1}{x}$ 2. $a x^{2} + b x + x - c + \frac{d}{x} - \frac{e}{x ^{2}}$ 3. $3 x^{2} - 5 x + ab$ 4. $\frac{2}{x ^{2} - a x + b ^{3}}$ 5. $\frac{1}{x} - \frac{2}{x + 5}$ Which of the above are rational expressions?
1. A.1, 4 and 5 only
2. B.1, 3, 4 and 5 only
3. C.2, 4 and 5 only
4. D.1 and 2 only
Show answer
Answer: B
Q1032018 · 22 Apr 2018
In a Binomial distribution, the mean is three times its variance. What is the probability of exactly 3 successes out of 5 trials?
1. A.80/243
2. B.40/243
3. C.20/243
4. D.10/243
Show answer
Answer: A
Q1042018 · 22 Apr 2018
Consider the following statements: 1. $P (\overset{ˉ}{A} \cup B) = P (\overset{ˉ}{A}) + P (B) - P (\overset{ˉ}{A} \cap B)$ 2. $P (A \cap \overset{ˉ}{B}) = P (B) - P (A \cap B)$ 3. $P (A \cap B) = P (B) P (A ∣ B)$ Which of the above statements are correct?
1. A.1 and 2 only
2. B.1 and 3 only
3. C.2 and 3 only
4. D.1, 2 and 3
Show answer
Answer: B
Q1052018 · 22 Apr 2018
The probabilities that a student will solve Question A and Question B are 0.4 and 0.5 respectively. What is the probability that he solves at least one of the two questions?
1. A.0.6
2. B.0.7
3. C.0.8
4. D.0.9
Show answer
Answer: B
Q1062018 · 22 Apr 2018
Two fair dice are rolled. What is the probability of getting a sum of 7?
1. A.1/36
2. B.1/6
3. C.7/12
4. D.5/12
Show answer
Answer: B
Q1072018 · 22 Apr 2018
If A and B are two events such that $2 P (A) = 3 P (B)$ , where $0 < P (A) < P (B) < 1$ , then which one of the following is correct?
1. A. $P (A ∣ B) < P (B ∣ A) < P (A \cap B)$
2. B. $P (A \cap B) < P (B ∣ A) < P (A ∣ B)$
3. C. $P (B ∣ A) < P (A ∣ B) < P (A \cap B)$
4. D. $P (A \cap B) < P (A ∣ B) < P (B ∣ A)$
Show answer
Answer: Dropped in the final answer key (full marks to everyone)
Q1082018 · 22 Apr 2018
A box has ten chits numbered 0, 1, 2, 3, ..., 9. First, one chit is drawn at random and kept aside. From the remaining, a second chit is drawn at random. What is the probability that the second chit drawn is “9”?
1. A.1/10
2. B.1/9
3. C.1/90
4. D.None of the above
Show answer
Answer: A
Q1092018 · 22 Apr 2018
One bag contains 3 white and 2 black balls, another bag contains 5 white and 3 black balls. If a bag is chosen at random and a ball is drawn from it, what is the chance that it is white?
1. A.3/8
2. B.49/80
3. C.8/13
4. D.1/2
Show answer
Answer: B
Q1102018 · 22 Apr 2018
Consider the following in respect of two events A and B: 1. P(A occurs but not B) = P(A) $-$ P(B) if $B \subset A$ 2. P(A alone or B alone occurs) = P(A) + P(B) $- P (A \cap B)$ 3. $P (A \cup B)$ = P(A) + P(B) if A and B are mutually exclusive Which of the above is/are correct?
1. A.1 only
2. B.1 and 3 only
3. C.2 and 3 only
4. D.1 and 2 only
Show answer
Answer: B
Q1112018 · 22 Apr 2018
A committee of three has to be chosen from a group of 4 men and 5 women. If the selection is made at random, what is the probability that exactly two members are men?
1. A.5/14
2. B.1/21
3. C.3/14
4. D.8/21
Show answer
Answer: A
Q1122018 · 22 Apr 2018
If $n \in N$ , then $12 1^{n} - 2 5^{n} + 190 0^{n} - (- 4)^{n}$ is divisible by which one of the following?
1. A.1904
2. B.2000
3. C.2002
4. D.2006
Show answer
Answer: B