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

Required Probability in the lowest terms as fractions =
`(15)/(182) =0.0824`

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_{} } = (n!)/((n-r)!r!) = (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 =
`(n(E))/(n(S))`

`Required probability = (n(E))/(n(S)) = (60)/(792)`

Required Probability in the lowest terms as fractions =
`(15)/(182) =0.0824`