Question

How many ways are there to distribute 15 cookies between5 children such that:

(a) zero or more cookies?

(b) at least 1 cookie?

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In answering a question on a multiple choice test, a studenteither knows the answer or the student just guesses. Suppose that theprobability that the student knows the answer is 0.75, and the probabil-ity that he guesses is 0.25. Assume that the probability that the student’sguesses will be correct is 0.20. What is the conditional probability thatthe student guessed the answer to a question given that he answered itcorrectly?

Answer 1

Distribution of 15 cookies between 5 children is analogous to the number of solutions of the equation

x1 + x2 + x3 + x4 + x5 = 15

(a) No. of ways when all children receives zero or more cookies is = 19C4 = 3876

(b) No. of ways when all children recieves atleast 1 cookie = = 14C4 = 1001

Probability of correct answer = 0.75 + 0.25*0.20 = 0.80

The required conditional probability = P(G | C)

= P(C | G)*P(G)/P(C)

= (0.25*0.20)/0.80

= 1/16 = 0.0625