Probability · NDA previous year questions

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.$\frac{1}{6}$

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.$P(A\cap B)+P(B\cap C)+P(C\cap A)-2P(A\cap B\cap C)$
4. D.$P(A\cap B)+P(B\cap C)+P(C\cap A)-3P(A\cap B\cap C)$

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.$\frac{1}{6}$

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.$\frac{1}{6}$

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.$\frac{1}{3}$

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

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.$\frac{7}{17}$

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.$\frac{4}{3},\frac{16}{9}$

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 $P(A\mid B)$?

1. A.$\frac{1}{5}$
2. B.$\frac{1}{6}$
3. C.$\frac{2}{5}$
4. D.$\frac{1}{3}$

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

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.$P(A)P(B)$

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.$\frac{2}{11}$

Let A, B and C be three mutually exclusive and exhaustive events associated with a random experiment. If $P(B)=1.5P(A)$ and $P(C)=0.5P(B)$, then $P(A)$ is equal to

1. A.$\frac{3}{4}$
2. B.$\frac{4}{13}$
3. C.$\frac{2}{3}$
4. D.$\frac{1}{2}$

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.$\frac{34}{39}$

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.$\frac{229}{256}$

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.$\frac{1}{32}$

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. $P(\bar{A})+P(\bar{B})=2-2p-q$ 2. $P(\bar{A}\cap \bar{B})=1-p-q$ 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

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.$\frac{25}{121}$

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

Consider the following expressions: 1. $x+x^2-\frac{1}{x}$ 2. $\sqrt{a{x}^2+bx+x-c+\frac{d}{x}-\frac{e}{x^2}}$ 3. $3x^2-5x+ab$ 4. $\frac{2}{x^2-ax+b^3}$ 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

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

Consider the following statements: 1. $P(\bar{A}\cup B)=P(\bar{A})+P(B)-P(\bar{A}\cap B)$ 2. $P(A\cap \bar{B})=P(B)-P(A\cap B)$ 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

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

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

If A and B are two events such that $2P(A)=3P(B)$, 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.$P(A\cap B)<P(A|B)<P(B|A)$