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, two green ones, five 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 has at least one green one.

Solutions

Expert Solution

Total marbles = 4 + 2 + 5 + 2 = 13

total number of ways to choose 8 marbles out of 13 = 13C8 = 13! / (8! * (13 - 8)!) = 1287

total green marbles = 2

total non-green marbles = 13 - 2 = 11

P(at least one green) = 1 - P(no green)

= 1 - (11C8 / 13C8)

= 1 - (165 / 1287)

= 1122 / 1287

= 34 / 39

orchestra answered 11 months ago

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