# Sample Spaces and Events

• April 3rd 2009, 12:13 AM
youvy
Sample Spaces and Events
43. From a group of 20 men and 16 women, 2 people are chosen at random. Find the probability of:

a) 1 man and 1 woman being chosen
b) 2 men being chosen
c) 2 women being chosen

Thank you:)
• April 3rd 2009, 12:35 AM
toop
a. 1 man being chosen = 20/36 and 1 woman being chosen is 16/36

The probability of both would be the product of the two probabilities I believe.

b. The probability of the first man being chosen is 20/36 and the probability of the second is 19/35 since you are now one man down. Multiply the two probabilities.

c. The probability of the first woman being chosen is 16/36 and the second is 15/35. Multiply the two like above.
• April 3rd 2009, 03:19 AM
mr fantastic
Quote:

Originally Posted by toop
a. 1 man being chosen = 20/36 and 1 woman being chosen is 16/36

The probability of both would be the product of the two probabilities I believe.

b. The probability of the first man being chosen is 20/36 and the probability of the second is 19/35 since you are now one man down. Multiply the two probabilities.

c. The probability of the first woman being chosen is 16/36 and the second is 15/35. Multiply the two like above.

I don't think your solution to (a) is correct.

The correct answer is given by $\frac{{20 \choose 1} \cdot {16 \choose 1}}{{36 \choose 2}} = \frac{20 \cdot 16 \cdot 2}{36 \cdot 35} \, ....$