Probability · NDA previous year questions

Suppose that there is a chance for a newly constructed building to collapse, whether the design is faulty or not. The chance that the design is faulty is 10%. The chance that the building collapses is 95% if the design is faulty, otherwise it is 45%. If it is seen that the building has collapsed, then what is the probability that it is due to faulty design?

1. A.0.10
2. B.0.19
3. C.0.45
4. D.0.95

A fair coin is tossed 6 times. What is the probability of getting a result in the $6^{\text{th}}$ toss which is different from those obtained in the first five tosses ?

1. A.$\frac{7}{16}$
2. B.$\frac{1}{16}$
3. C.$\frac{1}{32}$
4. D.$\frac{1}{64}$

In a class, there are n students including the students P and Q. What is the probability that P and Q sit together if seats are assigned randomly?

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

Consider the following for the next items that follow: Three boys P, Q, R and three girls S, T, U are to be arranged in a row for a group photograph. What is the probability that all three boys sit together?

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

Consider the following for the next items that follow: Three boys P, Q, R and three girls S, T, U are to be arranged in a row for a group photograph. What is the probability that boys and girls sit alternatively?

1. A.$\frac{4}{5}$
2. B.$\frac{1}{10}$
3. C.$\frac{5}{6}$
4. D.$\frac{1}{7}$

Consider the following for the next items that follow: Three boys P, Q, R and three girls S, T, U are to be arranged in a row for a group photograph. What is the probability that no two girls sit together?

1. A.$\frac{2}{5}$
2. B.$\frac{3}{5}$
3. C.$\frac{1}{18}$
4. D.$\frac{1}{5}$

Consider the following for the next items that follow: Three boys P, Q, R and three girls S, T, U are to be arranged in a row for a group photograph. What is the probability that P and Q take the two end positions?

1. A.$\frac{1}{15}$
2. B.$\frac{7}{15}$
3. C.$\frac{14}{15}$
4. D.$\frac{11}{45}$

Consider the following for the next items that follow: Three boys P, Q, R and three girls S, T, U are to be arranged in a row for a group photograph. What is the probability that Q and U sit together?

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

Let A and B be two independent events such that P(A̅) = 0.7, P(B̅) = k, P(A ∪ B) = 0.8, what is the value of k ?

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

A biased coin with the probability of getting head equal to $\frac{1}{4}$ is tossed five times. What is the probability of getting tail in all the first four tosses followed by head ?

1. A.$\frac{81}{512}$
2. B.$\frac{81}{1024}$
3. C.$\frac{81}{256}$
4. D.$\frac{27}{1024}$

A coin is biased so that heads comes up thrice as likely as tails. In four independent tosses of the coin, what is probability of getting exactly three heads ?

1. A.$\frac{81}{256}$
2. B.$\frac{27}{64}$
3. C.$\frac{27}{256}$
4. D.$\frac{9}{256}$

Let X and Y be two random variables such that $X+Y=100$. If X follows Binomial distribution with parameters $n=100$ and $p=\frac{4}{5}$, what is the variance of Y?

1. A.1
2. B.$\frac{1}{2}$
3. C.16
4. D.$\frac{1}{16}$

The observations 4, 1, 4, 3, 6, 2, 1, 3, 4, 5, 1, 6 are outputs of 12 dices thrown simultaneously. If m and M are means of lowest 8 observations and highest 4 observations respectively, then what is (2m + M) equal to ?

1. A.10
2. B.12
3. C.17
4. D.21

A die is thrown 10 times and obtained the following outputs : 1, 2, 1, 1, 2, 1, 4, 6, 5, 4 What will be the mode of data so obtained ?

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

One bag contains 3 white and 2 black balls, another bag contains 2 white and 3 black balls. Two balls are drawn from the first bag and put it into the second bag and then a ball is drawn from the second bag. What is the probability that it is white ?

1. A.$\frac{6}{7}$
2. B.$\frac{32}{70}$
3. C.$\frac{3}{10}$
4. D.$\frac{1}{70}$

Three dice are thrown. What is the probability that each face shows only multiples of 3 ?

1. A.$\frac{1}{9}$
2. B.$\frac{1}{18}$
3. C.$\frac{1}{27}$
4. D.$\frac{1}{3}$

What is the probability that the month of December has 5 Sundays ?

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

A natural number n is chosen from the first 50 natural numbers. What is the probability that $n+\frac{50}{n}<50$ ?

1. A.$\frac{23}{25}$
2. B.$\frac{47}{50}$
3. C.$\frac{24}{25}$
4. D.$\frac{49}{50}$

What is the probability of getting a composite number in the list of natural numbers from 1 to 50?

1. A.$\frac{7}{10}$
2. B.$\frac{17}{25}$
3. C.$\frac{18}{25}$
4. D.$\frac{33}{50}$

If n > 7, then what is the probability that C(n, 7) is a multiple of 7?

1. A.0
2. B.$\frac{1}{7}$
3. C.$\frac{1}{2}$
4. D.1

Two numbers x and y are chosen at random from a set of the first 10 natural numbers. What is the probability that (x + y) is divisible by 4 ?

1. A.$\frac{1}{5}$
2. B.$\frac{2}{9}$
3. C.$\frac{8}{45}$
4. D.$\frac{7}{45}$

A number x is chosen at random from first n natural numbers. What is the probability that the number chosen satisfies $x+\frac{1}{x}>2$ ?

1. A.$\frac{1}{n}$
2. B.$\frac{1}{(2n)}$
3. C.$\frac{(n-1)}{n}$
4. D.1

Three fair dice are tossed once. What is the probability that they show different numbers that are in AP?

1. A.$\frac{1}{12}$
2. B.$\frac{1}{18}$
3. C.$\frac{1}{36}$
4. D.$\frac{1}{72}$

If P(A) = 0.5, P(B) = 0.7 and P(A ∩ B) = 0.3, then what is the value of P(A' ∩ B') + P(A' ∩ B) + P(A ∩ B') ?

1. A.0.6
2. B.0.7
3. C.0.8
4. D.0.9

Five coins are tossed once. What is the probability of getting at most four tails ?

1. A.$\frac{31}{32}$
2. B.$\frac{15}{16}$
3. C.$\frac{29}{32}$
4. D.$\frac{7}{8}$