What is the probability of exactly 4 greens

Question

1. Major political parties in Australia are Labor, Liberal and Greens. About 10% are thought to be supporting Greens. A survey asked 20 people what party they support.
1) What is the probability that exactly 4 people will support Greens?

2) What is the probability that more than 6 people support Greens?

Answer 1

I will tell you the formulae for the answers; you will need to do the arithmetic.

 

This presumably is a binomial density problem with n = 20, p = .1 and q = .9

 

With this assumption the first probability is ₂₀C₄ * (.1)⁴ * (.9)¹⁶.

 

The second probability is the sum of ₂₀C_k * (.1)^k * (.9)^20-k from k = 70 to 20.

 

Note: _nC_r is the binomial coefficient of n things taken r at a time.

 

The sum you need in the second part is sometimes printed in tables in probability textbooks, although it is not too difficult to calculate with a spreadsheet