Question

Recall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing four red marbles, three green ones, two white ones, and three purple ones. She grabs five of them. Find the probability of the following event, expressing it as a fraction in lowest terms. HINT [See Example 1.] She has two red ones and one of each of the other colors.

Answer 1

[TeX] \frac{5}{22}[/TeX]

Explanation:

Red=4

Green=3

White=2

Purple=3

Total=4+3+2+3=12

She wants to pick 5 out of 12 marbles from.

n(S)=12C5=792

Let A= Event of Picking 2 Red, and one of each of the other colours.

n(A)=(5C2)*(3C1)*(2C1)*(3C1)

=10*3*2*3=180

Therefore:

[TeX]P(A)= \frac{n(A)}{n(S)}[/TeX]

[TeX]= \frac{180}{792}[/TeX]

[TeX] \frac{5}{22}[/TeX]

The Probability of picking two reds and one of each other color is [TeX]\frac{5}{22}[/TeX].