A box contains 4 red balls, 8 green balls, 12 orange balls, and 7 yellow balls....
A box contains 4 red balls, 8 green balls, 12 orange balls, and 7 yellow balls. If 7 balls are randomly selected from the box without replacement, then find these probabilities. Show your work to receive credit.
a. P(3 are green balls)
b. P(2 are red balls and 3 are orange balls)
Homework Answers
Total balls = 4 + 8 + 12 + 7 = 31
In general, x items are selected from n items by nCx ways,
Where nCx = n! / [ (n-x)! * x! ]
a)
P(3 are green balls) = 8C3 * 23C4 / 31C7
= 56 * 8855 / 2629575
= 0.1886
b)
P(2 are red balls and 3 are orange balls) = 4C2 * 12C3 * 15C2 / 31C7
= 6 * 220 * 105 / 2629575
= 0.0527
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