9. For a random experiment with three possible outcomes A1, A2, A3 which of the following gives a legitimate probability assignment? (a) P( A1)=1/2, P( A2)=1/3, P(A3 )= 1/3. (b) P( A1)=1/2, P( A2)=1/6, P(A3)= 1/6. (c) P( A1 )=1/2, P( A2)=2/5, P(A3 )= 1/10. (d) P( A1)=1/2, P( A2 )=3/4, P(A3)= -1/4.

Suppose the sensitivity of a diagnostic procedure to test whether a person has a particular disease is 95 % . A person who actually has the disease is tested for it using this procedure by two independent laboratories. (1) What is the probability that both test results will be positive? (ii) What is the probability that at least one of the two test results willI be positive?

According to an almanac, 80% of adult smokers started smoking before turning 18 years old. (a) Compute the mean and standard deviation of the random variable X, the number of smokers who started before 18 in 300 trials of the probability experiment. (b) Interpret the mean. (c) Would it be unusual to observe 255 smokers who started smoking before turning 18 years old in a random sample of 300 adult smokers? Why? D= 1 (e) O, =(Round to the nearest tenth as needed.) (b) What is the correct interpretation of the mean? O A. It is expected that in a random sample of 300 adult smokers, 240 will have started smoking before turning 18. O B. It is expected that in a random sample of 300 adult smokers, 240 will have started smoking after turning 18. OC. It is expected that in 50% of random samples of 300 adult smokers, 240 will have started smoking before turning 18. (c) Would it be unusual to observe 255 smokers who started smoking before turning 18 years old in a random sample of 300 adult…

Let E and F be two events of an experiment with sample space S. Suppose P(E) = 0.46, P(F^) = 0.65, and P(E U F) =0.7. Calculate the probabilities below. (a) P(E) = (b) P(F) (c) P(E n F) =