Question

Nine popular brands of beer are used in a blind taste study for consumer recognition. Complete parts (A) and (B) below. (A) If 3 distinct brands are chosen at random from the 9 and if a consumer is not allowed to repeat any answers, what is the probability that all 3 brands could be identified by just guessing? Let the sample space S be the set of ways that the 3 distinct brands can be chosen from the 9 popular brands of beer. The number of elements in the sample space S is n(S) = (Type a whole number.) The probability is (Type an integer or a simplified fraction.) (B) If repeats are allowed in the 3 brands chosen at random from the 9 and if a consumer is allowed to repeat answers, what is the probability that all 3 brands are identified correctly by just guessing? The probability is . (Type an integer or a simplified fraction.)

Answer 1

Answer:

Given,

n(S) = 9

P(Choosing 1st beer) = 1/9

P(Choosing 2nd beer) = 1/8

P(3rd beer) = 1/7

P(All 3 beers) = 1/9 * 1/8 * 1/7

= 1/(9*8*7)

= 1/504

= 0.002

b)

P(Choosing 3 beers with repetition) = (1/9)^3

= 1/729

= 0.0013