Question

Suppose you have a group of 12 British people and 18 Americans. What is the probability of randomly selecting a four-person committee consisting entirely of Americans? Round to 4 decimals.

Answer 1

It is given that we have a group of 12 British people and 18 Americans. We have to choose 4 random people to form a committee.

We have to find the probability of randomly selecting a four-person committee consisting entirely of Americans. In other words, we have to find the probability such that in a committee there is all American person. So,

There are total 18+12=30 person group.

Total no. of cases=³⁰C₄  and total no. of favourable cases= ¹⁸C₄*¹²C₀. Thus,

Required probability =