Question

A city council consists of eight Democrats and two Republicans. If a committee of seven people is selected, find the probability of selecting three Democrats and four Republicans.

a) 0.0036
b) 0.0288
c) 0.0576
d) 0.288

Answer 1

The probability of selecting three Democrats and four Republicans in the committee is approximately 0.0933.

Step-by-step explanation:

This is a hypergeometric problem because we are choosing a committee from a group of eight Democrats and two Republicans. To find the probability of selecting three Democrats and four Republicans in a committee of seven, we need to use the hypergeometric probability formula:

P(X=k) = (C(m, k) * C(N-m, n-k)) / C(N, n)

Where:

• P(X=k) is the probability of selecting k Democrats and n-k Republicans
• m is the number of Democrats
• N is the total number of people in the committee (m + r)
• n is the number of people to be selected for the committee

Plugging in the values:

P(X=3) = (C(8, 3) * C(2, 4-3)) / C(10, 7)

P(X=3) = (56 * 2) / 120

P(X=3) = 0.0933

So, the probability of selecting three Democrats and four Republicans in the committee is approximately 0.0933.