Probability · NDA previous year questions

Three dice are thrown. What is the probability of getting a triplet?

1. A.$\frac{1}{6}$
2. B.$\frac{1}{18}$
3. C.$\frac{1}{36}$
4. D.$\frac{1}{72}$

Consider the following statements: 1. If $A$ and $B$ are exhaustive events, then their union is the sample space. 2. If $A$ and $B$ are exhaustive events, then their intersection must be an empty event. 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

What is the number of outcomes when a coin is tossed and then a die is rolled only in case a head is shown on the coin?

1. A.6
2. B.7
3. C.8
4. D.None of the above

If $P(A)=\frac{2}{3},P(B)=\frac{2}{5}$ and $P(A\cup B)-P(A\cap B)=\frac{2}{5}$, then what is $P(A\cap B)$ equal to?

1. A.$\frac{3}{5}$
2. B.$\frac{5}{11}$
3. C.$\frac{1}{3}$
4. D.None of the above

What is the probability that there are 5 Mondays in the month of February 2016?

1. A.0
2. B.$\frac{1}{7}$
3. C.$\frac{2}{7}$
4. D.None of the above

In a relay race, there are six teams $A,B,C,D,E$ and $F$. What is the probability that $A,B,C$ finish first, second, third respectively?

1. A.$\frac{1}{2}$
2. B.$\frac{1}{12}$
3. C.$\frac{1}{60}$
4. D.$\frac{1}{120}$

Consider a random experiment of throwing together a die and two coins. The associated sample space has

1. A.8 points
2. B.12 points
3. C.24 points
4. D.36 points

In throwing a six faced dic, let A be the event that an even number occurs, B be the event that an odd number occurs and C be the event that a number greater than 3 occurs. Which one of the following is correct ?

1. A.A and C are mutually exclusive
2. B.A and B are mutually exclusive
3. C.B and C are mutually exclusive
4. D.A, B and C are mutually exclusive

What is the probability of getting a sum of 7 with two dice ?

1. A.1/6
2. B.1/3
3. C.1/12
4. D.5/36

Four coins are tossed simultaneously. What is the probability of getting exactly 2 heads ?

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

A bag contains 5 black and 3 white balls. Two balls are drawn at random one after the other without replacement. What is the probability that both are white ?

1. A.1/28
2. B.1/14
3. C.3/28
4. D.None of the above

If A and B are any two events such that $P(\overline{A})=0.4$, $P(\overline{B})=0.3$, $P(A\cup B)=0.9$, then what is the value of $P(\overline{A}\cup \overline{B})$ equal to ?

1. A.0.2
2. B.0.5
3. C.0.6
4. D.0.7

A fair coin is tossed repeatedly. The probability of getting a result in the fifth toss different from those obtained in the first four tosses is

1. A.1/2
2. B.1/32
3. C.31/32
4. D.1/16

Two numbers are successively drawn from the set U = {1, 2, 3, 4, 5, 6, 7, 8}, the second being drawn without replacing the first. The number of elementary events in the sample is

1. A.64
2. B.56
3. C.32
4. D.14

If P(E) denotes the probability of an event E, then E is called certain event if :

1. A.P(E) = 0
2. B.P(E) = 1
3. C.P(E) is either 0 or 1
4. D.P(E) = 1/2

What is the probability that a leap year selected at random will contain 53 Mondays ?

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

If A and B are two events such that $P(A\cup B)=\frac{3}{4}$, $P(A\cap B)=\frac{1}{4}$, $P(\overline{A})=\frac{2}{3}$ where $\overline{A}$ is the complement of A, then what is P(B) equal to ?

1. A.1/3
2. B.2/3
3. C.1/9
4. D.2/9

Three coins are tossed simultaneously. What is the probability that they will fall two heads and one tail ?

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

Which one of the following is correct ?

1. A.An event having no sample point is called an elementary event
2. B.An event having one sample point is called an elementary event
3. C.An event having two sample points is called an elementary event
4. D.An event having many sample points is called an elementary event

What is the most probable number of successes in 10 trials with probability of success 2/3 ?

1. A.10
2. B.7
3. C.5
4. D.4

What is the probability that both balls are of same colour ?

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

What is the probability of getting at least one green ball ?

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

Two dice each numbered from 1 to 6 are thrown together. Let A and B be two events given by A : even number on the first die B : number on the second die is greater than 4 What is $P(A\cup B)$ equal to ?

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

What is $P(A\cap B)$ equal to ?

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

Consider the following statements: 1. A continuous random variable can take all values in an interval. 2. A random variable which takes a finite number of values is necessarily discrete. 3. Construction of a frequency distribution is based on data which are discrete. Which of the above statements are correct?

1. A.1 and 2 only
2. B.2 and 3 only
3. C.1 and 3 only
4. D.1, 2 and 3