Drawer A contains five pennies and three dimes Drawer B has

Drawer A contains five pennies and three dimes. Drawer B has three pennies and seven dimes. Drawer and coin are selected at random.

a) Find P(selecting a dime)

b) Suppose dime is obtained. Find P(dime came from drawer B)

Solution

a)

By Bayes\' Rule,

P(dime) = P(A) P(dime|A) + P(B) P(dime|B)

Thus,

P(dime) = (1/2)(3/8) + (1/2)(7/10)

P(dime) = 0.5375 [answer]

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b)

P(B|dime) = P(B and dime) / P(B)

As

P(B and dime) = P(B) P(dime|B) = (1/2)(7/10) = 0.35

Then

P(B|dime) = 0.35/0.5375 = 0.651162791 [ANSWER]