FINAL EXAM MATH 276 FALL 2017 DR W R JAVIER YOUR NAME INSTRUCTIONS: ABSOLUTELY N

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FINAL EXAM MATH 276 FALL 2017 DR W R JAVIER YOUR NAME INSTRUCTIONS: ABSOLUTELY NO CELL PHONES, ELECTRONIC RECORDING DEVICES; USE BLANK SHEETS OF PAPER TO WRITE YOUR WORK ON; PLEASE DO NOT WRITE ANYTHING ON THIS PAPER OTHER THAN YOUR NAME. PLEASE DO WRITE YOUR WORK IN SEQUENCE: (a)FOLLOWED BY (2).ETC (1)(8 pts; 4 pts each) IF P(A) = .3 and P(B)-, 1 then find (a) The smallest possible value for P(AnB) (b) The largest possible value for P(AnB) (2)( 8pts) IF A and B are independent and P(A)-.3 and P(A B) = . I then find P(B) = ? (3) (10 pts, 5 pts each)Of a population of consumers, 60% are reputed to prefer a particular brand A, of toothpaste. If a sequence of randomly chosen people are interviewed, find the probability that (a) exactly 5 people will have to be interviewed to encounter the first consumer who prefers brand a? (b) At least 5 people will have to be interviewed to encounter the first consumer who prefers brandA? (4%12 pts; 4 pts each)Customers arriving in a department store according to a Poisson distribution at an average of 7 per hour. During a given hour, what are the probabilities that (a) no more than 3 customers arrive (b) at least two customers arrive (c) exactly 5 customers arrive

Explanation / Answer

1) P(A) = 0.3, P(B) = 0.1

a) smallest value for P(A and B) = 0

b) largest value of P(A and B) = min (P(A), P(B) )= 0.1

2) P(A) = 0.3

P(A and B) = 0.1

when A and B are independent

P(A and B) = P(A) * P(B)

hence 0.1 = 0.3 * P(B)

P(B) = 1/3

P(B bar) = 1- P(B) = 2/3

Post rest questions again, you are supposed to ask only one question at a time

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