Algebra 2 probability

Question

A bag contains 1 green, 4 red, and 5 yellow balls. Two balls are selected at random. Find P (1 red and 1 green).

Answer 1

The probability is the ratio between the number of desired pairs

and the number of all pairs.

First, for the desired pairs there is just one way to chose the green ball

and four ways to chose the red ball.

Therefore there are 4 desired pairs.

Secondly, the total number of pairs is "10 chose 2", which is

10x9/2 = 45

Therefore the probability is 4/45.

Answer 2

G = green ball

R = red ball

Y = yellow ball

We are looking at combinations, C(n, k).

# of red/green pairs = 4*1 = 4

# of random pairs = C(10, 2) = 45

P(1 red and 1 green) = 4/45 ≈ 0.0889

The probability of selecting two balls (1 red and 1 green) at random is about 0.0889