Probability · NDA previous year questions

The probability that a student passes Physics test is 2/3 and the probability that he passes both Physics test and English test is 11/15. The probability that he passes at least one test is 4/5 What is the probability that he passes English test?

1. A.11/15
2. B.13/15
3. C.14/15
4. D.1

An event X can happen with probability p and event Y can happen with probability q. Further, X and Y are independent events. Which of the following statements is/are correct? I. The probability that exactly one of the events happens is p + q - pq II. The probability that at least one of the events happens is p + q - 2pq Select the answer using the code given below.

1. A.I only
2. B.II only
3. C.Both I and II
4. D.Neither I nor II

Three faces of a die are black, two faces are white and one face is red. The die is tossed three times. What is the probability that the colours black, white and red appear in the first, second and third tosses respectively?

1. A.1/36
2. B.1/6
3. C.7/36
4. D.5/36

A fair coin is tossed 4 times. What is the probability that two heads do not occur consecutively?

1. A.1/8
2. B.3/8
3. C.7/16
4. D.1/2

In a throw of three dice, what is the probability of getting one prime number, one composite number and one number which is neither prime nor composite?

1. A.1/2
2. B.1/3
3. C.1/4
4. D.1/6

An integer is chosen at random from the first 50 integers. What is the probability that the integer is neither divisible by 5 nor 9?

1. A.7/10
2. B.18/25
3. C.37/50
4. D.19/25

Out of 50 consecutive natural numbers, two integers are chosen at random. What is the probability that their sum is odd?

1. A.1/2
2. B.24/49
3. C.1/4
4. D.25/49

Let X be a random variable following binomial distribution with parameters n = 5 and p = k Further, P(X = 1) = 0.4096 and P(X = 2) = 0.2048 . What is the value of k?

1. A.0.2
2. B.0.25
3. C.0.3
4. D.0.35

What is the value of k?

1. A.1/2
2. B.1/3
3. C.1/4
4. D.1/5

What is the value of P * (X = 3) ^ 0

1. A.135/1024
2. B.5/128
3. C.45/1024
4. D.70/1024

Consider the following for the two (02) items that follow: A committee of 6 members is formed from a group of 7 gentlemen and 4 ladies. What is the probability that the committee includes exactly 3 gentlemen?

1. A.10/33
2. B.30/77
3. C.100/231
4. D.5/11

What is the probability that the committee includes at least 2 ladies?

1. A.41/66
2. B.47/66
3. C.49/66
4. D.53/66

Consider the following for the two (02) items that follow: The probabilities that A, B and C become managers are 3/10 1/2 and 4/5 respectively. The probabilities that bonus scheme will be introduced if A, B and C become managers are 4/9, 2/9 and 1/3 respectively. What is the probability that the bonus scheme will be introduced?

1. A.17/45
2. B.19/45
3. C.23/45
4. D.26/45

If the bonus scheme has been introduced, then what is the probability that the manager appointed was B?

1. A.5/23
2. B.6/23
3. C.7/23
4. D.8/23

If two fair dice are tossed, then what is the probability that the sum of the numbers on the faces of the dice is strictly greater than 7?

1. A.1/3
2. B.5/12
3. C.7/12
4. D.3/4

The probability of a man hitting a target is 1/5. If the man fires 7 times, then what is the probability that he hits the target at least twice?

1. A.$1-\left(\frac{3}{5}\right){\left(\frac{4}{5}\right)}^6$
2. B.$1-\left(\frac{3}{5}\right){\left(\frac{4}{5}\right)}^7$
3. C.$1-\left(\frac{11}{5}\right){\left(\frac{4}{5}\right)}^6$
4. D.$1-\left(\frac{11}{5}\right){\left(\frac{4}{5}\right)}^7$

Let X be a random variable following binomial distribution whose mean and variance are 200 and 160 respectively. What is the value of the number of trials (n)?

1. A.500
2. B.1000
3. C.1500
4. D.2000

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

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

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

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

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

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

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

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