7. In each part, find P(Y 3) a. A bowl contains 50 coins, 10 Canadian dimes and

Question

7. In each part, find P(Y 3) a. A bowl contains 50 coins, 10 Canadian dimes and 40 US dimes. A coin is selected at random, the type of coin is noted, and then the coin is returned to the bowl. The experiment is repeated 5 times. Let Y denote the number of Canadian dimes selected. b. A bowl contains 50 coins, 10 Canadian dimes and 40 US dimes. A coin is selected at random, the type of coin is noted, and then the coin is set aside. The experiment is repeated 5 times. Let Y denote the number of Canadian dimes selected. c. A bowl contains 50 coins, 10 Canadian dimes and 40 US dimes. A coin is selected at random, the type of coin is noted, and then the coin is returned to the bowl. The experiment is repeated until a Canadian dime is selected. Let Y denote the number of times that the experiment is performed. d. It is known that 1000 square yard bolts of a certain material have an average of 30 flaws per bolt. A customer purchases 8 square yards of the material. Let Y be the number of flaws in the material which was purchased. Assume that Y follows a Poisson distribution.

Explanation / Answer

a)
p = 10/50 = 0.2
Y follows binomial distribution with n = 5 , p = 0.2
P(Y = 3) = 5C3 * p^3*(1-p)^2
=0.0512

b)
3 canadian coins 2 others
P(Y =3)

= 5C2 * 10 * 9 * 40 * 39 * 38 /(50 *49*48 *47*46)

= 10*10 * 9 * 40 * 39 * 38 /(50 *49*48 *47*46)

= 0.20983

c)
P(Y = 3)
it means the first two coins are not canadian
0.8^2*0.2
= 0.128

d) 30 flaws per 1000 square
hence 8 square yards have 30/1000*8 = 0.24

P(Y= 3) = 0.0018123

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