Probability · NDA previous year questions

Three fair dice are thrown. What is the probability of getting a total greater than or equal to 15 ?

1. A.$\frac{19}{216}$
2. B.$\frac{1}{12}$
3. C.$\frac{17}{216}$
4. D.$\frac{5}{54}$

The probability that a person hits a target is 0.5. What is the probability of at least one hit in 4 shots ?

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

During war, one ship out of 5 was sunk on an average in making a certain voyage. What is the probability that exactly 3 out of 5 ships would arrive safely?

1. A.$\frac{16}{625}$
2. B.$\frac{32}{625}$
3. C.$\frac{64}{625}$
4. D.$\frac{128}{625}$

A card is drawn from a pack of 52 cards. A gambler bets that it is either a spade or an ace. The odds against his winning are

1. A.9 ∶ 4
2. B.35 ∶ 17
3. C.17 ∶ 35
4. D.4 ∶ 9

The completion of a construction job may be delayed due to strike. The probability of strike is 0.6. The probability that the construction job gets completed on time if there is no strike is 0.85 and the probability that the construction job gets completed on time if there is a strike is 0.35. What is the probability that the construction job will not be completed on time ?

1. A.0.35
2. B.0.45
3. C.0.55
4. D.0.65

Two digits out of 1, 2, 3, 4, 5 are chosen at random and multiplied together. What is the probability that the last digit in the product appears as 0?

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

Consider the following data for the next three (03) items that follow : There are 90 applicants for a job. Some of them are graduates. Some of them have less than three years experience. $$\begin{array}{lcc}& \text{Number of graduates}& \text{Number of non-graduates}\\ \text{At least 3 years experience}& 18& 9\\ \text{Less than 3 years experience}& 36& 27\end{array}$$ Let G be the event that the first applicant interviewed is a graduate and T be the event that first applicant interviewed has at least 3 years experience. What is $P(G\cap \overline{T})$ equal to?

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

Consider the following data for the next three (03) items that follow : There are 90 applicants for a job. Some of them are graduates. Some of them have less than three years experience. $$\begin{array}{lcc}& \text{Number of graduates}& \text{Number of non-graduates}\\ \text{At least 3 years experience}& 18& 9\\ \text{Less than 3 years experience}& 36& 27\end{array}$$ Let G be the event that the first applicant interviewed is a graduate and T be the event that first applicant interviewed has at least 3 years experience. What is $P(G|\overline{T})$ equal to?

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

Consider the following data for the next three (03) items that follow : There are 90 applicants for a job. Some of them are graduates. Some of them have less than three years experience. $$\begin{array}{lcc}& \text{Number of graduates}& \text{Number of non-graduates}\\ \text{At least 3 years experience}& 18& 9\\ \text{Less than 3 years experience}& 36& 27\end{array}$$ Let G be the event that the first applicant interviewed is a graduate and T be the event that first applicant interviewed has at least 3 years experience. What is $P(\overline{T}|\overline{G})$ equal to?

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

Consider the following data for the next three (03) items that follow : The incidence of suffering from a disease among workers in an industry has a chance of $33\frac{1}{3}\%$. What is the probability that exactly 3 out of 6 workers suffer from a disease?

1. A.$\frac{80}{729}$
2. B.$\frac{10}{81}$
3. C.$\frac{10}{243}$
4. D.$\frac{160}{729}$

Consider the following data for the next three (03) items that follow : The incidence of suffering from a disease among workers in an industry has a chance of $33\frac{1}{3}\%$. What is the probability that no one out of 6 workers suffers from a disease?

1. A.$\frac{665}{729}$
2. B.$\frac{64}{729}$
3. C.$\frac{4}{243}$
4. D.$\frac{1}{729}$

Consider the following data for the next three (03) items that follow : The incidence of suffering from a disease among workers in an industry has a chance of $33\frac{1}{3}\%$. What is the probability that at least one out of 6 workers suffer from a disease ?

1. A.$\frac{728}{729}$
2. B.$\frac{665}{729}$
3. C.$\frac{653}{729}$
4. D.$\frac{596}{729}$

Suppose 20 distinct points are placed randomly on a circle. Which of the following statements is/are correct? 1. The number of straight lines that can be drawn by joining any two of these points is 380. 2. The number of triangles that can be drawn by joining any three of these points is 1140. 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

Consider the following relations for two events E and F : 1. P(E ∩ F) ≥ P(E) + P(F) - 1 2. P(E ∪ F) = P(E) + P(F) + P(E ∩ F) 3. P(E ∪ F) ≤ P(E) + P(F) Which of the above relations is/are correct?

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

If P(A|B) < P(A), then which one of the following is correct?

1. A.P(B|A) < P(B)
2. B.P(B|A) > P(B)
3. C.P(B|A) = P(B)
4. D.P(B|A) > P(A)

A problem is given to three students A, B and C, whose probabilities of solving the problem independently are $\frac{1}{2}$, $\frac{3}{4}$ and p respectively. If the probability that the problem can be solved is $\frac{29}{32}$, then what is the value of p?

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

In a cricket match, a batsman hits a six 8 times out of 60 balls he plays. What is the probability that on a ball played he does not hit a six?

1. A.$\frac{2}{3}$
2. B.$\frac{1}{15}$
3. C.$\frac{2}{15}$
4. D.$\frac{13}{15}$

3-digit numbers are formed using the digits 1, 3, 7 without repetition of digits. A number is randomly selected. What is the probability that the number is divisible by 3?

1. A.0
2. B.$\frac{1}{3}$
3. C.$\frac{1}{4}$
4. D.$\frac{1}{8}$

What is the probability that the roots of the equation $x^2+x+n=0$ are real, where $n\in \mathbb{N}$ and $n<4$?

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

If A and B are two events such that $P(\text{not }A)=\frac{7}{10}$, $P(\text{not }B)=\frac{3}{10}$ and $P(A|B)=\frac{3}{14}$, then what is $P(B|A)$ equal to?

1. A.$\frac{11}{14}$
2. B.$\frac{9}{14}$
3. C.$\frac{1}{4}$
4. D.$\frac{1}{2}$

Seven white balls and three black balls are randomly placed in a row. What is the probability that no two black balls are placed adjacently?

1. A.$\frac{7}{15}$
2. B.$\frac{8}{15}$
3. C.$\frac{11}{15}$
4. D.$\frac{13}{15}$

Let two events A and B be such that P(A) = L and P(B) = M. Which one of the following is correct?

1. A.$P(A|B)<\frac{L+M-1}{M}$
2. B.$P(A|B)>\frac{L+M-1}{M}$
3. C.$P(A|B)\ge \frac{L+M-1}{M}$
4. D.$P(A|B)=\frac{L+M-1}{M}$

If $\mathrm{P}(\mathrm{A}\cup \mathrm{B})=\frac{5}{6}$, $\mathrm{P}(\mathrm{A}\cap \mathrm{B})=\frac{1}{3}$ and $\mathrm{P}(\bar{\mathrm{A}})=\frac{1}{2}$, then which of the following is/are correct? 1. A and B are independent events. 2. A and B are mutually exclusive events. 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

A coin is tossed twice. If E and F denote occurrence of head on first toss and second toss respectively, then what is P(E ∪ F) equal to?

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

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

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