Probability · NDA previous year questions

2020 10 questions

1. Q1022020 · 6 Sept 2020

   If three dice are rolled under the condition that no two dice show the same face, then what is the probability that one of the faces is having the number 6 ?

   1. A.$\frac{5}{6}$
   2. B.$\frac{5}{9}$
   3. C.$\frac{1}{2}$
   4. D.$\frac{5}{12}$
   Show answer

   Answer: C

2. Q1032020 · 6 Sept 2020

   If $P(A\cup B)=\frac{5}{6}$, $P(A\cap B)=\frac{1}{3}$ and $P(\text{not }A)=\frac{1}{2}$, then which one of the following is not correct?

   1. A.$P(B)=\frac{2}{3}$
   2. B.$P(A\cap B)=P(A)P(B)$
   3. C.$P(A\cup B)>P(A)+P(B)$
   4. D.$P(\text{not }A\text{ and not }B)=P(\text{not }A)P(\text{not }B)$
   Show answer

   Answer: C

3. Q1112020 · 6 Sept 2020

   What is the probability that February of a leap year selected at random, will have five Sundays?

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

   Answer: B

4. Q1132020 · 6 Sept 2020

   A husband and wife appear in an interview for two vacancies for the same post. The probability of the husband's selection is $\frac{1}{7}$ and that of the wife's selection is $\frac{1}{5}$. If the events are independent, then the probability of which one of the following is $\frac{11}{35}$?

   1. A.At least one of them will be selected
   2. B.Only one of them will be selected
   3. C.None of them will be selected
   4. D.Both of them will be selected
   Show answer

   Answer: A

5. Q1142020 · 6 Sept 2020

   A dealer has a stock of 15 gold coins out of which 6 are counterfeit. A person randomly picks 4 of the 15 gold coins. What is the probability that all the coins picked will be counterfeit?

   1. A.$\frac{1}{91}$
   2. B.$\frac{4}{91}$
   3. C.$\frac{6}{91}$
   4. D.$\frac{15}{91}$
   Show answer

   Answer: A

6. Q1152020 · 6 Sept 2020

   A committee of 3 is to be formed from a group of 2 boys and 2 girls. What is the probability that the committee consists of 2 boys and 1 girl?

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

   Answer: D

7. Q1162020 · 6 Sept 2020

   In a lottery of 10 tickets numbered 1 to 10, two tickets are drawn simultaneously. What is the probability that both the tickets drawn have prime numbers?

   1. A.$\frac{1}{15}$
   2. B.$\frac{1}{2}$
   3. C.$\frac{2}{15}$
   4. D.$\frac{1}{5}$
   Show answer

   Answer: C

8. Q1182020 · 6 Sept 2020

   Consider a random variable $X$ which follows Binomial distribution with parameters $n=10$ and $p=\frac{1}{5}$. Then $Y=10-X$ follows Binomial distribution with parameters $n$ and $p$ respectively given by

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

   Answer: D

9. Q1192020 · 6 Sept 2020

   If $A$ and $B$ are two events such that $P(A)=0.6$, $P(B)=0.5$ and $P(A\cap B)=0.4$, then consider the following statements: 1. $P(\bar{A}\cup B)=0.9$. 2. $P(\bar{B}\mid \bar{A})=0.6$. 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
   Show answer

   Answer: D

10. Q1202020 · 6 Sept 2020

    Three cooks $X$, $Y$ and $Z$ bake a special kind of cake, and with respective probabilities 0.02, 0.03 and 0.05, it fails to rise. In the restaurant where they work, $X$ bakes 50%, $Y$ bakes 30% and $Z$ bakes 20% of cakes. What is the proportion of failures caused by $X$?

    1. A.$\frac{9}{29}$
    2. B.$\frac{10}{29}$
    3. C.$\frac{19}{29}$
    4. D.$\frac{28}{29}$
    Show answer

    Answer: B