Recall from Example 1 that whenever Su2an sees a bag of marb

Recall from Example 1 that whenever Su2an sees a bag of marbles, she grabs a handful at random. She has seen a bag containing four red marbles, four green ones, three white ones, and two purple ones. She grabs eight of them. Find the probability of the following event, expressing it as a fraction in lowest terms. She does not have all the red ones.

Solution

Solution:

Number of ways to choose 5 marbles out of 13 = 13C5 = 1287

Now for the events

We need to find the number ways that Suzan cannot get all of the red marbles.

let\'s calculate first She has all the red ones

Since there are four red ones and she’s grabbing five marbles, the fifth marble must come from the non-red marbles. We can view this as a sequence of steps, where the first step in the sequence is to choose all the red ones.

Number of ways to choose 4 red marbles out of 4 = 4C4 = 1

Number of ways to choose 1 other marble out of remaining 9 = 9C1 = 9

Number of ways to choose 4 red marbles AND 1 remaining marble = 6 * 9 = 54

So, the probability is = 54/1287 = 6/143

Suzan cannot get all of the red marbles = 1 - the probability of all all the red ones = 1- 6/143 = 137/143

Answer : 137/143