On each workday, the manager of a company sends one of his 3 secretaries (either

Question

On each workday, the manager of a company sends one of his 3 secretaries (either Amy, Zoe, or Moe) out to get coffee. The chance that Amy will be sent on any day is two times as great as the chance that Zoe will be sent, and two times as great as the chance that Moe will be sent. When Amy goes for the coffee, there is a .05 chance that it will be cold when she returns. For either Zoe or Moe, this chance is .1.

a) On any workday, what is the probability that Amy goes for the coffee?

b) On any workday, what is the probability that the coffee comes back cold?

c) Given that the coffee comes back cold, what is the probability that Amy went for the coffee?

Explanation / Answer

a) let probability for Amy =x =2*probability for Zoe=2*probability for Moe

as sum of pobability is 1

hence x+x/2+x/2 =1

x =0.5

a)) therefore probability that Amy goes for the coffee =P(Amy) =0.5

b)  probability that the coffee comes back cold =P(Amy goes and coffee come back cold+Zoe goes and coffee come back cold+Moe goes and coffee come back cold)

=0.5*0.05+0.25*0.1+0.25*0.1=0.075

c) probability that Amy went for the coffee given coffee comes back cold

=P(Amy goes and coffee come back cold)/P(coffee come back cold) =0.05*0.05/0.075 =1/3

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