Part I Poker dice is played by simultaneously rolling 5 dice. What is the probability of obtaining A. no two alike? B. one pair? C. three of a kind? D. four of a kind? E. ve of a kind? Part II A medical procedure has a total success rate of 98%. Out of all patients, 85% are in group A and 15% are in group B. For patients in group B. the success rate is only 96%. If a random patient is chosen and it is found that she is in group A. what is the probability that the procedure will be a success? Part III An insurance company writes a policy which states that if an event E occurs within a year then an amount A should be paid. The company estimates the probability of E happening within a year to be p. They want the expected prot to be 10% of A. What should they charge the customer? Part IV Let X be a normally distributed random variable with mean 5. Suppose that P(X > 9) : 0.2. Compute Var(X)