A particular type of tennis racket comes in a midsize version and an oversize ve

Question

A particular type of tennis racket comes in a midsize version and an oversize version. 70% of all customers who order this racket from a certain store purchase the oversize version, and 30% purchase the midsize version.

a) If 6 of the first 8 orders are for oversize rackets, on average, how many of the first 100 rackets will be for oversize rackets?

b) If 6 of the first 8 orders are for oversize rackets, what is the probability that the 8th oversize racket ordered is the 12th racket ordered overall?

Explanation / Answer

a) There are 92 orders remaining, Expected number of oversize rackets, E = 0.7*92 = 64.4

Out of 100 rackets, on average 70.4 or 70 orders are for oversize rackets

b) There are 4 orders remaining for 12 orders out of which 2 oversize orders are required for the 8th oversize racket.

1 out of 3 orders need to be for oversize racket.
P(1 out of 3 oversize racket) = 3C1 * 0.7 * 0.32 = 0.189
P(8th oversize racket on 12th racket ordered overall) = 0.189 * 0.7 = 0.1323

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