Probability · NDA previous year questions

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

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

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

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

If $n\in N$, then $121^n-25^n+1900^n-(-4{)}^n$ is divisible by which one of the following?

1. A.1904
2. B.2000
3. C.2002
4. D.2006

A committee of two persons is selected from two men and two women. The probability that the committee will have exactly one woman is

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

Let a die be loaded in such a way that even faces are twice likely to occur as the odd faces. What is the probability that a prime number will show up when the die is tossed?

1. A.$\frac{1}{3}$
2. B.$\frac{2}{3}$
3. C.$\frac{4}{9}$
4. D.$\frac{5}{9}$

Let the sample space consist of non-negative integers up to 50, $X$ denote the numbers which are multiples of 3 and $Y$ denote the odd numbers. Which of the following is/are correct? 1. $P(X)=\frac{8}{25}$ 2. $P(Y)=\frac{1}{2}$ 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

For two events $A$ and $B$, let $P(A)=\frac{1}{2}$, $P(A\cup B)=\frac{2}{3}$ and $P(A\cap B)=\frac{1}{6}$. What is $P(\bar{A}\cap B)$ equal to?

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

Let $A$ and $B$ be two events with $P(A)=\frac{1}{3}$, $P(B)=\frac{1}{6}$ and $P(A\cap B)=\frac{1}{12}$. What is $P(B|\bar{A})$ equal to?

1. A.$\frac{1}{5}$
2. B.$\frac{1}{7}$
3. C.$\frac{1}{8}$
4. D.$\frac{1}{10}$

In a binomial distribution, the mean is $\frac{2}{3}$ and the variance is $\frac{5}{9}$. What is the probability that $X=2$?

1. A.$\frac{5}{36}$
2. B.$\frac{25}{36}$
3. C.$\frac{25}{216}$
4. D.$\frac{25}{54}$

The probability that a ship safely reaches a port is $\frac{1}{3}$. The probability that out of 5 ships, at least 4 ships would arrive safely is

1. A.$\frac{1}{243}$
2. B.$\frac{10}{243}$
3. C.$\frac{11}{243}$
4. D.$\frac{13}{243}$

What is the probability that at least two persons out of a group of three persons were born in the same month (disregard year)?

1. A.$\frac{33}{144}$
2. B.$\frac{17}{72}$
3. C.$\frac{1}{144}$
4. D.$\frac{2}{9}$

If $P(B)=\frac{3}{4}$, $P(A\cap B\cap \bar{C})=\frac{1}{3}$ and $P(\bar{A}\cap B\cap \bar{C})=\frac{1}{3}$, then what is $P(B\cap C)$ equal to?

1. A.$\frac{1}{12}$
2. B.$\frac{3}{4}$
3. C.$\frac{1}{15}$
4. D.$\frac{1}{9}$

In a multiple-choice test, an examinee either knows the correct answer with probability $p$, or guesses with probability $1-p$. The probability of answering a question correctly is $\frac{1}{m}$, if he or she merely guesses. If the examinee answers a question correctly, the probability that he or she really knows the answer is

1. A.$\frac{mp}{1+mp}$
2. B.$\frac{mp}{1+(m-1)p}$
3. C.$\frac{(m-1)p}{1+(m-1)p}$
4. D.$\frac{(m-1)p}{1+mp}$

Five sticks of length 1, 3, 5, 7 and 9 feet are given. Three of these sticks are selected at random. What is the probability that the selected sticks can form a triangle?

1. A.0.5
2. B.0.4
3. C.0.3
4. D.0

A committee of two persons is constituted from two men and two women. What is the probability that the committee will have only women?

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

A question is given to three students $A,B$ and $C$ whose chances of solving it are $\frac{1}{2}$, $\frac{1}{3}$ and $\frac{1}{4}$ respectively. What is the probability that the question will be solved?

1. A.$\frac{1}{24}$
2. B.$\frac{1}{4}$
3. C.$\frac{3}{4}$
4. D.$\frac{23}{24}$

For two dependent events $A$ and $B$, it is given that $P(A)=0.2$ and $P(B)=0.5$. If $A\subseteq B$, then the values of conditional probabilities $P(A|B)$ and $P(B|A)$ are respectively

1. A.$\frac{2}{5},\frac{3}{5}$
2. B.$\frac{2}{5},1$
3. C.$1,\frac{2}{5}$
4. D.Information is insufficient

A card is drawn from a well-shuffled ordinary deck of 52 cards. What is the probability that it is an ace?

1. A.$\frac{1}{13}$
2. B.$\frac{2}{13}$
3. C.$\frac{3}{13}$
4. D.$\frac{1}{52}$

Consider the following statements: 1. Two events are mutually exclusive if the occurrence of one event prevents the occurrence of the other. 2. The probability of the union of two mutually exclusive events is the sum of their individual probabilities. 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

If two fair dice are thrown, then what is the probability that the sum is neither 8 nor 9?

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

Let $A$ and $B$ are two mutually exclusive events with $P(A)=\frac{1}{3}$ and $P(B)=\frac{1}{4}$. What is the value of $P(\overline{A}\cap \overline{B})$?

1. A.$\frac{1}{6}$
2. B.$\frac{1}{4}$
3. C.$\frac{1}{3}$
4. D.$\frac{5}{12}$

A point is chosen at random inside a circle. What is the probability that the point is closer to the centre of the circle than to its boundary?

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

A random sample of 20 people is classified in the following table according to their ages: | Age | Frequency | |---|---| | 15 - 25 | 2 | | 25 - 35 | 4 | | 35 - 45 | 6 | | 45 - 55 | 5 | | 55 - 65 | 3 | What is the mean age of this group of people?

1. A.41.0
2. B.41.5
3. C.42.0
4. D.42.5