MBA 604 Introduction Probaility and Statistics Lecture Notes

(ii) Find P (B c ).
(iii) Find P (A ∩ B).
(iv) Find P (A ∪ B).
(v) Are B and C independent events? Justify your answer.
(vi) Are B and C mutually exclusive events? Justify your answer.
(vii) Are C and D independent events? Justify your answer.
(viii) Are C and D mutually exclusive events? Justify your answer.
6. Use the laws of probability to justify your answers to the following questions:
(i) If P (A ∪ B) =.6, P (A) =.2, and P (B) =.4, are A and B mutually exclusive?
independent?
(ii) If P (A ∪ B) =.65, P (A) =.3, and P (B) =.5, are A and B mutually exclusive?
independent?
(iii) If P (A ∪ B) =.7, P (A) =.4, and P (B) =.5, are A and B mutually exclusive?
independent?
7. Suppose that the following two weather forecasts were reported on two local TV
stations for the same period. First report: The chances of rain are today 30%, tomorrow
40%, both today and tomorrow 20%, either today or tomorrow 60%. Second report: The
chances of rain are today 30%, tomorrow 40%, both today and tomorrow 10%, either
today or tomorrow 60%. Which of the two reports, if any, is more believable? Why? No
credit if answer is not justified. (Hint: Let A and B be the events of rain today and rain
tomorrow.)
8. A box contains five balls, a black (b), white (w), red (r), orange (o), and green (g).
Three balls are to be selected at random.
(i) Find the sample space S (Hint: there is 10 sample points).
S = {bwr, ···}
(ii) Find the probability of selecting a black ball.
(iii) Find the probability of selecting one black and one red ball.
9. A box contains four black and six white balls.
(i) If a ball is selected at random, what is the probability that it is white? black?
(ii) If two balls are selected without replacement, what is the probability that both
balls are black? both are white? the first is white and the second is black? the first is
black and the second is white? one ball is black?
(iii) Repeat (ii) if the balls are selected with replacement.
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