For the remainder of this problem, suppose that Grace can send an email message (M) to the recruiter at PWC to say hello, or not (NM). Grace figures that if she would be offered a position, then the response from the recruiter will be friendly (F) with probability 2/3, and if she would not be offered a position, then the recruiter's response will be unfriendly (U) with probability 2/3. Suppose that the recruiter always responds to such an email, and the email can easily be categorized into friendly or unfriendly. The student summer salary rate at PWC is $12000. 8. Compute the probability that the recruiter will send a friendly response. 9. Suppose that Grace decides to send an email to the recruiter at PWC, who sent her back a friendly response. What is probability that Grace will receive an offer from PwC? Provide your probability as a decimal number. 10. Consider the following partially-filled decision tree. For each of the following probabilities, indicate which branch in the decision tree it should be placed in (or not placed at all). Select the best answer. a. P(A) b. P(J) E C. P(M) d. P(U)