Question

Imagine you and Janice are the only ones working as telemarketers for a large cooperation. You make 70% of the calls and each call takes you Exponential amount of time with parameter λ1 = 2 hrs-1 . Janice, on the other hand, makes the remaining 30% of total calls. Each call takes her Exponential amount of time with parameter λ2 = 4 hrs-1 . A certain call was made 30 minutes ago and it is still ongoing. What is the probability that you made this call?

Answer 1

The probability that you made this call is 0.8639.

Step-by-step explanation:

Parameter for you = λ1 = 2

⇒ β1 = 1 / λ1 = 1 / 2 = 0.5

Parameter for Janice = λ2 = 4

⇒ β2 = 1 / λ2 = 1 / 4 = 0.25

Probability that you made a for 0.5 hours or more:

`P(X\geq 0.5)=e^(-0.5/0.5)=0.3679`

Probability that Janice made a for 0.5 hours or more:

`P(X\geq 0.5)=e^(-0.5/0.25)=0.1353`

Overall probability that a call was made for 0.5 hours of more

= (0.7 x 0.3679) + (0.3 x 0.1353)

= 0.2981

Probability that you made the given call

= 0.7 x 0.3679 / 0.2981

= 0.8639