Probability · NDA previous year questions

2022 19 questions

1. Q1022022 · 4 Sept 2022

   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.$\frac{33}{50}$
   Show answer

   Answer: B

2. Q1032022 · 4 Sept 2022

   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
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   Answer: B

3. Q1042022 · 4 Sept 2022

   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.$\frac{7}{45}$
   Show answer

   Answer: B

4. Q1052022 · 4 Sept 2022

   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
   Show answer

   Answer: C

5. Q1062022 · 4 Sept 2022

   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.$\frac{1}{72}$
   Show answer

   Answer: B

6. Q1072022 · 4 Sept 2022

   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
   Show answer

   Answer: B

7. Q1082022 · 4 Sept 2022

   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.$\frac{7}{8}$
   Show answer

   Answer: A

8. Q1092022 · 4 Sept 2022

   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.$\frac{5}{54}$
   Show answer

   Answer: D

9. Q1102022 · 4 Sept 2022

   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.$\frac{7}{8}$
   Show answer

   Answer: C

10. Q1122022 · 4 Sept 2022

    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.$\frac{128}{625}$
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    Answer: D

11. Q1132022 · 4 Sept 2022

    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
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    Answer: A

12. Q1152022 · 4 Sept 2022

    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
    Show answer

    Answer: B

13. Q1012022 · 10 Apr 2022

    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.$\frac{4}{5}$
    Show answer

    Answer: B

14. Q1122022 · 10 Apr 2022

    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.$\frac{4}{5}$
    Show answer

    Answer: B

15. Q1132022 · 10 Apr 2022

    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.$\frac{5}{7}$
    Show answer

    Answer: C

16. Q1142022 · 10 Apr 2022

    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.$\frac{3}{4}$
    Show answer

    Answer: D

17. Q1152022 · 10 Apr 2022

    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.$\frac{160}{729}$
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    Answer: D

18. Q1162022 · 10 Apr 2022

    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.$\frac{1}{729}$
    Show answer

    Answer: B

19. Q1172022 · 10 Apr 2022

    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.$\frac{596}{729}$
    Show answer

    Answer: B