Question

Kristina Karganova invites 15 relatives to a​ party: her​ mother, 4 ​aunts, 2 uncles, 3 ​brothers, 1 male​ cousin, and 4 female cousins. If the chances of any one guest arriving first are equally​ likely, find the probabilities that the first guest to arrive is as follows.

​(a) A brother or an uncle

​(b) A brother or a cousin

​(c) A brother or her mother

Answer 1

(a)

Mother : 1 No.

Aunts : 4 Nos.

Uncles: 2 Nos.

Brothers: 3 Nos.

Male cousin: 1 No.

Female cousin: 4 Nos.

Total : 15 Nos.

P(A brother OR An Uncle) = P(A brother) + P(An Uncle) = 3/15 + 2/15 = 5/15 = 1/3 = 0.3333

(b)

P(A brother OR A Cousin) = P(A brother OR A Male cousin OR A Female cousin) = P(A brother) + P(A Male cousin) + P(A Female cousin)= 3/15 + 1/15 +4/15 = 8/15 = 0.5333

(c)

P(A brother OR Mother) = P(A brother) + P(Mother) = 3/15 + 1/15 = 4/15 = 0.2667