1. The probably of carrying a cancer mutation in the general population is 1 in 1000.What is the probability of finding no one with the mutation in a random sample of 500 people?

2. A new test for colorectal cancer in adults is marketed with 99% sensitivity and 95% specificity.That is if a tested patient has colorectal cancer, the test correctly reports 'positive result' 99% of the time, and if a tested patient does not have colorectal cancer, the test correctly reports 'negative result' 95% of the time.The prevalence of colorectal cancer in adults is 1% (i.e. on average, one in 100 adults has colorectal cancer).What is the probability that an adult does not have colorectal cancer, if his test returns negative?

3. The probably of carrying a cancer mutation in the general population is 1 in 1000.What is the probability of finding 3 people with the mutation in a random sample of 500 people?(Hint: Poisson distribution is a good approximation of the binomial function when p is small).

4. Suppose that Y ~ Binomial (500, 0.02). Estimate Pr (Y = 16).(Hint: Poisson distribution is a good approximation of the binomial function when p is small).

5. Suppose X~Normal(140, 20).Calculate P(X ≥ 200).

6. Four people, A, B, C, and D, compete for a prize and only one of them can win.The chance that D wins is equal to the chance that either A or B wins.The chance that C wins is equal to the chance that A wins and is twice as much as the chance of B wins.What is the chance that either A or C will win the competition?

7. How many times does one need to roll a 6-sided die so that he can be 90% sure that a 6 will turn up?

8. What is the probability of getting at least one double (e.g. two ones) from two 6-sided dice, after rolling them 5 times?

9. A die is rigged so that it only rolls out even numbers.What is the sample space of the experiment in which the die is rolled once?

10. The probability of success of a Bernoulli trial is p. Which of the following is the definition of the geometric distribution?

11. X and Y are real-valued random variables, with expected values of E(X) and E(Y), respectively.What is the expected value of X - Y?

12. A 6-sided die is rolled once.What is the expected value of the outcome of the roll?

13. Which of the following is NOT a discrete random variable?

14. If X and Y are real-valued random variables and c is a constant, which of the following is false?

15. Calculate the cumulative distribution function at x = 1 for an exponential distribution with λ = 1.

16. Matt flipped a coin four times.What is the probability that he had exactly two heads?

17. A couple plans to have 4 children.They already have one girl.What is the probability that they will have 3 girls in total?

18. X is a random variable with a variance of 1.What is the variance of 5 ∙ X?

19. If X is a random variable with an expected value of 5, what is the expected value of 5 ∙ X?

20. What is a Bernoulli trial?

21. If X and Y are two independent random variables and E(X) and E(Y) are their expected values, respectively, then what is E(X ∙ Y)?

22. The average height of men in the U.S. is 1.8 m with a standard deviation of 8 cm.A random group of 16 men is selected.What is the probability that the average height of this group is higher than 1.84 m?

23. A continuous random variable X has the following cumulative distribution function: F(x) = x/5 for x between 0 and 5, F(x) = 0 for x < 0, and F(x) = 1 for x > 5.What is the probability of 4 ≥ X ≥ 3?

24. The average GPA of students at a university is 3.0 with a standard deviation of 1.0.A random sample of 9 students is collected.What is the probability that the average GPA of this sample is higher than 3.3?

25. One in 10 coins has tails on both sides.One coin is chosen at random and flipped three times.What is the probability of getting 3 heads?