Question

In: Statistics and Probability

Recall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful...

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, five 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.]

O BJECTIVE:

She has two red ones and one of each of the other colors.

Solutions

Expert Solution

Total no. of marbles in the bag = 15

Red = 4

Green = 3

White = 5

Purple = 3

She picks out 5 marbles.

Probability that she picks 2 red , 1 green , 1 Purple, 1 white =   

Now Since we are calculating Probability we need to Consider all the Same colour marbles as distinct marbles.

No. of ways to pick group of r things out of n things where order does not matter is given by combination   

So Total No of ways of choosing 5 marbles out of 15 marbles

No of ways to Pick 2 red out of 4 red marbles =

NO. of ways to Pick 1 green out of 3 green marbles =

No of ways to Pick 1 white out of 5 white marbles =

No of ways to Pick 1 purple out of 3 purple marbles =

NO . of way to choose 2 red , 1 green , 1 Purple, 1 white marbles together =   

Required probability =

orchestra answered 2 years ago
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