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 three red marbles, two green ones, five white ones, and two 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

Answer:

Required Probability in the lowest terms as fractions =  $\frac{15}{182} =0.0824$

Step-by-step explanation:

Step 1:-

Given Suzan has three red marbles, two green ones, five white ones, and two purple ones.

Total marbles = 3R+2G+5W+2P = 12

The number of exhaustive cases that the five marbles drawn from 12 marbles

n(S) = $12C_{5} = 792 ways$

by using formula $n_{Cr_{} } = \frac{n!}{(n-r)!r!} = \frac{12!}{(12-5)!5!}$   = 792

The number of favorable cases

She has drawn two red marbles from 3 red marbles, that is 3c₂ ways

she has drawn one  marble drawn from 2 green marbles, that is 2c₁ ways

she has drawn one  marble drawn from 5 white marbles, that is 5c₁ ways

she has drawn one  marble drawn from 2 purple marbles, that is 2c₁ ways

The favorable cases are (n(E) = 3c₂ X 2c₁X5c₁X2c₁ = 60 ways

Required Probability = $\frac{n(E)}{n(S)}$

$Required probability = \frac{n(E)}{n(S)} = \frac{60}{792}$

Required Probability in the lowest terms as fractions =  $\frac{15}{182} =0.0824$