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, four green ones, three white ones, and onepurple one. She grabs eight of them. Find the probability of the following event, expressing it as a fraction in lowest terms. HINT [See Example 1.]

She does not have all the red ones.

Answer 1

Solution:

For this problem is it best to let ? be the event that she does have all of the red ones, and then use the formula for finding the probability of a complement. To find the probability that she does get all the red ones, we must find two values: the total number of possible outcomes, ?(?), and the total number of favorable outcomes for the given event (getting all the red marbles). Since she is choosing 8 marbles from a total of 11, ?(?) = ?(11, 8) = 165. To get all the red ones, she must choose 3 red from 3, and then choose the remaining 5 marbles from the 8 non-red ones. There are ?(3,3)?(8, 5) = 56 ways to do this. Thus, ?(?) = 56 /165 . The probability of ? not occurring is then ?(? ′ ) = 1 − 56 /165 = 109/165 , so this is the probability that she does not get all the red ones.