Question

A toy chest contains 8 blonde barbies, 7 red haired barbies and 6 brunette barbies. 5 barbies are selected at random and there hair colors are noted. determine the following probabilities -

(a) P(all barbies are blonde) (b)P(exactly 2 barbies are red haired)(c)P(atleast one barbie is brunette.

Answer 1

A toy chest contains 8 blonde barbies, 7 red haired barbies and 6 brunette barbies giving a total of 8+7+6=21 dolls

Total number of ways of selecting 5 barbies is (order of selection is not important and hence this is combination)

(a) P(all barbies are blonde)

Number of ways of selecting 5 blonds (from 8 blonde barbies) and 0 others (from 13 dolls other than blond)  is

The probability of selecting all blond barbies is

ans: P(all barbies are blonde) is 0.0028

(b)P(exactly 2 barbies are red haired)

Number of ways of selecting 2 red haired (from 7 red haired barbies) and 3 others (from 14 dolls other than red haired)  is

The probability of selecting 2 red haired barbies is

ans: P(exactly 2 barbies are red haired)= 0.3756

(c)P(atleast one barbie is brunette)

Number of ways of selecting 0 brunette (from 6 brunette barbies) and 5 others (from 15 dolls other than brunette )  is

The probability of selecting at least one brunette is

ans: P(atleast one barbie is brunette) = 0.8524