A gambler faces three different slot machines, A, B and C, from which he randoml

Question

A gambler faces three different slot machines, A, B and C, from which he randomly picks one and plays the machine only once. The probability he will win if he plays machine A is 0.89. The probability he will win if he plays machine B is 0.29. The probability he will win if he plays machine C is 0.14. Use four decimals in your answers.

(a) What is the probability of this gambler winning?

(b) If he does win, what is the probability he played machine C?

(c) If he did not win, what is the probability he did play machine A?

Explanation / Answer

Probability of randomly picking a machine A = 1/3 , for machine B , P(B)=1/3 and for Machine C , P(C)=1/3

Given P(W|A) =0.89; P(W|B)=0.29; P(W|C) =0.13

a) Probability of gambler winning = [(1/3)*0.89] + [(1/3)*0.29] +[(1/3)*0.14]=0.44

b)if he does win probability he played machine c = P(W and C) /P(W) = [(1/3)*0.14]/0.44=0.106

c)If he didnt win, probability he did play machine A = P( NW and A)/P(NW) = [(1/3)*0.11]/(1-0.44)=0.0655

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