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

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 twopurple 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

= 1 / (12,8)* [ (4,3)*(3,2)*(2,1)*(3,1) + (4,4)*(3,1)*(2,2)*(3,1) + (4,3)*(3,2)*(2,1)*(3,2) + (4,3)*(4,3)*(2,1)*(3,1) + (4,2)*(3,3)*(2,2)*(3,1) + (4,2)*(3,2)*(2,2)*(3,2) + (4,1)*(3,3)*(2,2)*(3,2) ]

= [ 18+9+72+96+18+54+12 ] / 495

= 0.56