Question

Suppose there are two full bowls of cookies. Bowl has 20 chocolate chip and 10 oatmeal, while bowl H2 has 10 chocofute chip eookies and 20 oatmeal cookics. Our frend Bob picks a bowl at andoen, and then picks a cookie at random. We may aspume there is no remon to believe Bob treats one bowt differently from another, likewise for the cookies. The cookie turns out fo be an oatmeal cookie, Hfors probable is it that Bob picked it out of Bowd ?

Answer 1

The probability that Bob picked an oatmeal cookie from Bowl H is 1/2.

Step-by-step explanation:

To find the probability that Bob picked an oatmeal cookie from Bowl H, we need to use conditional probability. Let O1 be the event that Bob picked an oatmeal cookie and B be the event that Bob picked Bowl H. We are asked to find P(B|O1), i.e., the probability that Bob picked Bowl H given that he picked an oatmeal cookie.

Using Bayes' theorem, we have:

P(B|O1) = (P(O1|B) * P(B)) / P(O1)

P(O1|B) = 20/30 = 2/3 (since Bowl H has 10 oatmeal cookies out of 30 cookies)

P(B) = 1/2 (since there are 2 bowls)

P(O1) = (P(O1|B) * P(B)) + (P(O1|not B) * P(not B))

P(O1|not B) = 20/30 = 2/3 (since Bowl O has 20 oatmeal cookies out of 30 cookies)

P(not B) = 1/2 (since there are 2 bowls)

Plugging the values into the formula, we get:

P(B|O1) = ((2/3) * (1/2)) / (((2/3) * (1/2)) + ((2/3) * (1/2)))

After simplifying, we get:

P(B|O1) = 1/2