A jar comtains 30 green jelly beans and 20 purple Suppose 10

A jar comtains 30 green jelly beans and 20 purple. Suppose 10 jelly beans are selected at random from the jar.

a) Find P[obtaining exactly 5 purple jelly beans if they are selected with replacment]

b) Find P[obtaining exactly 5 purple jelly beans if they are selected without replacement]

Solution

There 50 beans, so there are 50C10 ways to choose any 10.

a)

P(5 purple with replacement) = P(purple)^5 = (20/50)^5 = 0.01024 [ANSWER]

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b)

P(5 purple without replacement) = (20/50)*(19/49)*(18/48)*(17/47)*(16/46) = 0.007317488 [ANSWER]