In: Statistics and Probability
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.
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