A jar contains 5 green jelly beans and 5 purple jelly beans. (a) Suppose one jel

Question

A jar contains 5 green jelly beans and 5 purple jelly beans.

(a) Suppose one jelly bean is to be selected at random. What is the value of p, the probability that a purple jelly bean is selected?

(b) Suppose 9 jelly beans are to be selected at random with replacement. Let X be the number of purple jelly beans in the selected. Calculate P(X = 1), the probability that there is exactly one purple jelly bean in the 9 selected.

(c) Now suppose 5 beans are to be selected at random without replacement. Let Y be the number of purple jelly beans in the selected. Calculate P(Y = 1), the probability that there is only one purple jelly bean in the 5 selected.

Explanation / Answer

A) Probability of purble jelly bean, p = 5/10 = 1/2

B) P(X=x) = nCx px pn-x

P(X=1) = 9C1 (1/2)1 x (1/2)8

= 0.0176

C) P(Y=1) = 5C1 x (5/10) x(5/9)x(4/8)x(3/7)x(2/6)

= 0.0992

Or

P(Y = 1) = 5C1 x 5C4/ 10C5 = 0.0992

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