Suppose there are two full bowls of cookies. Bowl one has 10 chocolate chip and 30 sugar cookies, while bowl two has 20 of each. Our friend Fred picks a bowl at random, and then picks a cookie at random. We may assume there is no reason to believe Fred treats one bowl differently from another, likewise for the cookies. The cookie turns out to be a sugar cookie. How probable is it that Fred picked it out of bowl one?

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Asked Oct 11, 2019
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  1. Suppose there are two full bowls of cookies. Bowl one has 10 chocolate chip and 30 sugar cookies, while bowl two has 20 of each. Our friend Fred picks a bowl at random, and then picks a cookie at random. We may assume there is no reason to believe Fred treats one bowl differently from another, likewise for the cookies. The cookie turns out to be a sugar cookie. How probable is it that Fred picked it out of bowl one?
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Expert Answer

Step 1

From the given information, number of bowls is 2, first bowl having 10 chocolate chip and 30 sugar cookies. The second bowl has 20 of each type.

Let A be the event that selecting cookie from first bowl 1 and B be the event selecting cookie from second bowl 2. E is the event that selecting sugar cookie.

The number of cookies in bowl 1=10+30=40

The number of cookies in bowl 2=20+20=40

Step 2

The P(A), P(B), P(E/A) and P(E/B) is obtained below:

The probability of selecting of bowl 1 is,

P(A) =1/2=0.50

The probability of selecting of bowl 2 is,

P(B) = 1/2 = 0.50

The probability that selecting sugar cookie from Bowl 1 is,

 P(E/A)=30/40=0.75

The probability that selecting sugar cookie from Bowl 2 is,

 P(E/B)=20/40=0.50

Step 3

The probability that Fred picked it out of bowl one is obtained below:

The required probabi...

P(ΕΙ Α)x P(A)
P(ΕA)P(A-PE B) xP(Β)
P(A E)
0.75x0.50
0.75x 0.500.50 x0.50
0.375
0.625
-0.60
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P(ΕΙ Α)x P(A) P(ΕA)P(A-PE B) xP(Β) P(A E) 0.75x0.50 0.75x 0.500.50 x0.50 0.375 0.625 -0.60

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