Probability · NDA previous year questions

353 questions asked across 18 exam years, newest first

Year-wise papers Topic-wise questions

Practise this topic

2024 28 questions

Q1032024 · 1 Sept 2024
Three distinct natural numbers chosen at random from 1 to 10. What is the probability that they are consecutive?
1. A.1/12
2. B.3/40
3. C.1/15
4. D.7/120
Show answer
Answer: C
Q1042024 · 1 Sept 2024
A, B, C are three mutually exclusive and exhaustive events associated with a random experiment. If 3P(B) = 4P(A) and 3P(C) = 2P(B), then what is P(A) equal to?
1. A.7/29
2. B.8/29
3. C.9/29
4. D.10/29
Show answer
Answer: C
Q1052024 · 1 Sept 2024
A die has two faces with number 4, three faces with number 5 and one face with number 6. If the die is rolled once, then what is the probability of getting 4 or 5?
1. A.1/3
2. B.2/3
3. C.5/6
4. D.1/2
Show answer
Answer: C
Q1062024 · 1 Sept 2024
A box contains 2 black, 4 yellow and 6 white balls. Three balls are drawn in succession with replacement. What is the probability that all three are of the same colour?
1. A.1/6
2. B.1/36
3. C.1/12
4. D.5/12
Show answer
Answer: A
Q1072024 · 1 Sept 2024
A can hit a target 5 times in 6 shots, B can hit 4 times in 5 shots and C can hit 3 times in 4 shots. What is the probability that A and C may hit but B may lose?
1. A.1/8
2. B.1/6
3. C.1/4
4. D.1/3
Show answer
Answer: A
Q1082024 · 1 Sept 2024
The letters of the word ZOOLOGY are arranged in all possible ways. What is the probability that the consonants and vowels occur alternatively?
1. A.6/35
2. B.3/35
3. C.2/35
4. D.1/35
Show answer
Answer: D
Q1092024 · 1 Sept 2024
A natural number x is chosen at random from the first 100 natural numbers. What is the probability that $x^{2} + x > 50$ ?
1. A.93/100
2. B.47/50
3. C.24/25
4. D.23/25
Show answer
Answer: B
Q1132024 · 1 Sept 2024
A fair coin is tossed till two heads occur in succession. What is the probability that the number of tosses required is less than 6?
1. A.5/64
2. B.15/32
3. C.31/64
4. D.19/32
Show answer
Answer: D
Q1142024 · 1 Sept 2024
Urn A contains 2 white and 2 black balls while urn B contains 3 white and 2 black balls. One ball is transferred from urn A to urn B and then a ball is drawn out of urn B. What is the probability that the ball is white?
1. A.11/20
2. B.7/12
3. C.3/5
4. D.1
Show answer
Answer: B
Q1152024 · 1 Sept 2024
For two events A and B, $P (A) = P (A ∣ B) = 0.25$ and $P (B ∣ A) = 0.5$ . Which of the following are correct? I. A and B are independent. II. $P (A^{c} \cup B^{c}) = 0.875$ III. $P (A^{c} \cap B^{c}) = 0.375$ Select the answer using the code given below.
1. A.I and II only
2. B.II and III only
3. C.I and III only
4. D.I, II and III
Show answer
Answer: D
Q1162024 · 1 Sept 2024
Two perfect dice are thrown. What C is the probability that the sum of the numbers on the faces is neither 9 nor 10?
1. A.1/36
2. B.5/36
3. C.7/36
4. D.29/36
Show answer
Answer: D
Q1172024 · 1 Sept 2024
The occurrence of a disease in an industry is such that the workers have 20% chance of suffering from it. What is the probability that out of 6 workers chosen at random, 4 or more will suffer from the disease?
1. A.53/3125
2. B.63/3125
3. C.73/3125
4. D.83/3125
Show answer
Answer: A
Q1182024 · 1 Sept 2024
Three perfect dice are rolled. Under the condition that no two show the same face, what is the probability that one of the faces shown is an ace (one)?
1. A.5/9
2. B.2/3
3. C.1/3
4. D.1/2
Show answer
Answer: D
Q1192024 · 1 Sept 2024
Three perfect dice $D_{1}$ , $D_{2}$ and $D_{3}$ are rolled. Let x, y and z represent the numbers on $D_{1}$ , $D_{2}$ and $D_{3}$ respectively. What is the number of possible outcomes such that $x < y < z$ ?
1. A.20
2. B.18
3. C.14
4. D.10
Show answer
Answer: A
Q1012024 · 21 Apr 2024
A bag contains 5 black and 4 white balls. A man selects two balls at random. What is the probability that both of these are of the same colour?
1. A. $\frac{1}{6}$
2. B. $\frac{5}{108}$
3. C. $\frac{4}{9}$
4. D. $\frac{5}{18}$
Show answer
Answer: C
Q1022024 · 21 Apr 2024
If a random variable $(x)$ follows binomial distribution with mean 5 and variance 4 , and $5^{23} P (X = 3) = λ 4^{λ}$ , then what is the value of $λ$ ?
1. A.3
2. B.5
3. C.23
4. D.25
Show answer
Answer: C
Q1062024 · 21 Apr 2024
If two random variables $X$ and $Y$ are connected by relation $\frac{2 X - 3 Y}{5 X + 4 Y} = 4$ and $X$ follows Binomial distribution with parameters $n = 10$ and $p = \frac{1}{2}$ , then what is the variance of $Y$ ?
1. A. $\frac{810}{361}$
2. B. $\frac{9}{19}$
3. C. $\frac{21}{361}$
4. D. $\frac{121}{361}$
Show answer
Answer: A
Q1072024 · 21 Apr 2024
An edible oil is sold at the rates 150, 200, 250, 300 rupees per litre in four consecutive years. Assuming that an equal amount of money is spent on oil by a family in every year during these years, what is the average price of oil in rupees (approximately) per litre?
1. A.210
2. B.220
3. C.230
4. D.240
Show answer
Answer: A
Q1082024 · 21 Apr 2024
If the letters of the word 'TIRUPATI' are written down at random, then what is the probability that both Ts are always consecutive?
1. A. $\frac{1}{2}$
2. B. $\frac{1}{4}$
3. C. $\frac{1}{7}$
4. D. $\frac{1}{14}$
Show answer
Answer: B
Q1092024 · 21 Apr 2024
Let $m = 7 7^{n}$ . The index $n$ is given a positive integral value at random. What is the probability that the value of $m$ will have 1 in the units place?
1. A. $\frac{1}{2}$
2. B. $\frac{1}{3}$
3. C. $\frac{1}{4}$
4. D. $\frac{1}{n}$
Show answer
Answer: C
Q1102024 · 21 Apr 2024
Three different numbers are selected at random from the first 15 natural numbers. What is the probability that the product of two of the numbers is equal to third number?
1. A. $\frac{1}{91}$
2. B. $\frac{2}{455}$
3. C. $\frac{1}{65}$
4. D. $\frac{6}{455}$
Show answer
Answer: C
Q1112024 · 21 Apr 2024
Consider the following for the next two (02) items that follow: Let $A$ and $B$ be two events such that $P (A \cup B) \geq 0.75$ and $0.125 \leq P (A \cap B) \leq 0.375$ . What is the minimum value of $P (A) + P (B)$ ?
1. A.0.625
2. B.0.750
3. C.0.825
4. D.0.875
Show answer
Answer: D
Q1122024 · 21 Apr 2024
Let $A$ and $B$ be two events such that $P (A \cup B) \geq 0.75$ and $0.125 \leq P (A \cap B) \leq 0.375$ . What is the maximum value of $P (A) + P (B)$ ?
1. A.0.75
2. B.1.125
3. C.1.375
4. D.1.625
Show answer
Answer: C
Q1132024 · 21 Apr 2024
Consider the following for the next two (02) items that follow: $A, B$ and $C$ are three events such that $P (A) = 0.6, P (B) = 0.4, P (C) = 0.5, P (A \cup B) = 0.8, P (A \cap C) = 0.3$ and $P (A \cap B \cap C) = 0.2$ and $P (A \cup B \cup C) \geq 0.85$ . What is the minimum value of $P (B \cap C)$ ?
1. A.0.1
2. B.0.2
3. C.0.35
4. D.0.45
Show answer
Answer: B
Q1142024 · 21 Apr 2024
Consider the following for the next two (02) items that follow: $A, B$ and $C$ are three events such that $P (A) = 0.6, P (B) = 0.4, P (C) = 0.5, P (A \cup B) = 0.8, P (A \cap C) = 0.3$ and $P (A \cap B \cap C) = 0.2$ and $P (A \cup B \cup C) \geq 0.85$ . What is the maximum value of $P (B \cap C)$ ?
1. A.0.1
2. B.0.2
3. C.0.35
4. D.0.45
Show answer
Answer: C