Question

What is the probability of:
a) randomly selecting a four-person committee consisting entirely of Americans from a pool of 12 british people and 18 Americans.
b) discovering your three best friends all have birthdays in April
c) getting a sum of 2,3, or 4 on a roll of two dice
d) randomly selecting a three-child family with either one or two girl children.

Answer 1

a) Total number of people = 12 + 18 = 30

We want to find probability of  four-person committee consisting entirely of Americans from a pool of 12 british people and 18 Americans.

Required probability = p = (18 * 17 * 16 * 15) / ( 30 * 29 * 28* 27) = 0.111658

Also we can used combinatrics formulae to find the above probability .

We select four people out of 30 people as ³⁰C₄ = 27405 ways

We select four people from 18 Americans in  ¹⁸C₄ = 3060 ways

So required probability = 3060/27405 = 0.111658

c) Total number of pairs = 6 * 6 = 36

Possible pair of sum 2, 3 or 5 are (1, 1) ; (1, 2); (2, 1); (3, 1) ; (1, 3) ; (2 , 2)

that is possible number of pairs = 6

So required probability = 6/36 = 1/6 = 0.166667

d) total numbe of girls(G)and boys(B) of three child families = 2*2*2 = 8

Possible number of ways of one or two girls are as GBB, BGB, BBG, GGB, GBG, BGG that is 6

So required probability = 6/8 = 3/4 = 0.75