Question

Pam is an employee at a jewelry kiosk in a mall. If Pam works hard, there is a 75% probability that jewelry profits will equal $400 a day and a 25% probability that jewelry profits will equal $200 a day. If Pam shirks, there is a 25% probability that jewelry profits will equal $400 a day and a 75% probability that jewelry profits will equal $200 a day. Suppose Pam is paid 50% of the daily jewelry profits. What is Pam’s expected gain from working hard?

Answer 1

175$

Explanation:

Given that Pam is an employee at a jewelry kiosk in a mall. If Pam works hard, there is a 75% probability that jewelry profits will equal $400 a day and a 25% probability that jewelry profits will equal $200 a day. If Pam shirks, there is a 25% probability that jewelry profits will equal $400 a day and a 75% probability that jewelry profits will equal $200 a day.

Since Pam works hard

expected value of profit for the kiosk =
`400(0.75)+200(0.25)\\=350`

From this value, 50% would be given to Pam

Hence expected gain for Pam for working hard

=
`0.5(350)\\=175`

175 $