Questions

L21. What is the sample space of 2 rolls of die and find the total number of events?

L22. Number of hours I study in a day is a discrete r.v. or continuous r.v.?

L23. Consider the roll of 6 sided die and two Events A ={1,2,3} & B={1,3,5}, find P(A|B)?

L24. A laboratory blood test is 95 percent effective in detecting a certain disease when it is, in fact, present. However, the test also yields a “false positive” result for 1 percent of the healthy persons tested. If .5 percent of the population actually has the disease, what is the probability that a person has the disease given that the test is positive?

L25. A fair 4-sided die is rolled twice and we assume that all sixteen possible outcomes are equally likely. Let X and Y be the result of the 1st and the

2nd roll, respectively. Where A={max(X,Y)=2} and B={min(X,Y)=2}. Find Events A & B are independent or not?

L31. Two rolls of 6 sided die such that P(i,j)=1/36. Three events A={1st roll is 1,2,3}, B={2nd roll is 3,4,5} & C={Sum of two rolls is 9} are given. Find these three events are independent or not?

L51: Suppose there is a dinner party, where n men check their hats. The hats got mixed up during dinner so that afterwards each man receives a random hat. The prob. each man gets his own hat is 1/n. Find the number of men who get their own hat? (Answer 1)

L61: Which following game would you play? Which game is better financially? (Hint: High variance means high risk)

Game A: We win $2 with probability 2/3 and lose $1 with probability 1/3.

Game B: We win $1002 with probability 2/3 and lose $2001 with probability 1/3.