CSAT Suneung · CSAT Mathematics

Probability, statistics and counting

22 practice questions, each with the answer and an explanation.

Practise Probability, statistics and counting now

Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 22 questions

  1. In how many ways can a committee of 2 be chosen from 6 students?
  2. In how many ways can a committee of 3 be chosen from 7 students?
  3. In how many ways can a committee of 3 be chosen from 8 students?
  4. In how many ways can a committee of 2 be chosen from 10 students?
  5. In how many ways can a committee of 4 be chosen from 9 students?
  6. 5 students stand in a row. Two particular students, Minho and Jisoo, must stand next to each other. How many arrangements are possible?
  7. 6 students stand in a row. Two particular students, Minho and Jisoo, must stand next to each other. How many arrangements are possible?
  8. 7 students stand in a row. Two particular students, Minho and Jisoo, must stand next to each other. How many arrangements are possible?
  9. For two events A and B, P(A) = 1/2, P(B) = 1/3 and P(A and B) = 1/6. What is P(A given B)?
  10. For two events A and B, P(A) = 3/5, P(B) = 1/2 and P(A and B) = 1/5. What is P(A given B)?
  11. For two events A and B, P(A) = 2/3, P(B) = 3/4 and P(A and B) = 1/2. What is P(A given B)?
  12. For two events A and B, P(A) = 1/4, P(B) = 1/2 and P(A and B) = 1/8. What is P(A given B)?
  13. A fair coin is tossed 4 times. What is the probability of exactly 2 heads?
  14. A fair coin is tossed 5 times. What is the probability of exactly 3 heads?
  15. In each play of a game the probability of winning is 1/3. In 3 plays, what is the probability of exactly 1 wins?
  16. In each play of a game the probability of winning is 1/3. In 4 plays, what is the probability of exactly 2 wins?
  17. A random variable X follows the normal distribution with mean 50 and standard deviation 8. Given that P(0 <= Z <= 1.5) = 0.4332, what is P(X >= 62)?
  18. X follows a normal distribution with mean 100 and standard deviation 10. Given that P(0 <= Z <= 2) = 0.4772, what is P(X >= 120)?
  19. The mean of a variable is 12 and its variance is 9. What is the mean of the new variable Y = 2X - 3?
  20. The variance of X is 9. What is the variance of Y = 2X - 3?
  21. What is the coefficient of x^2 in the expansion of (1 + x)^6?
  22. What is the constant term in the expansion of (x + 2/x)^4?

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