A family has a little boy A and two dogs D and C. None of them is fond of the ma

Question

A family has a little boy A and two dogs D and C. None of them is fond of the mailman. Given that they are outside, dogs D and C have a 30% and 40% chance, respectively, of biting the mailman. Boy A, if he is outside, has a 15% chance of doing the same thing. Suppose that only one of three is outside when the mailman comes.   

a). If D is outside 50% of time, C is 20% of time, and A is 30% of time, what is the probability that the mailman will be bitten?

b). Under these assumptions, if the mailman is bitten, what are the chances that boy A did it?

Explanation / Answer

Ans:

a)P(bitten)=P(bitten/D)*P(D)+P(bitten/C)*P(C)+P(bitten/A)*P(A)

=0.3*0.5+0.4*0.2+0.15*0.3

=0.275

b)

P(A/bitten)=P(bitten/A)*P(A)/P(bitten)=0.15*0.3/0.275=0.164

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