Question

1- If you are working with a discrete probability distribution, how does P(X≤5) compare with P(X<5)?

2- At a firm, the probability that an employee has completed a training program is P(T) = 0.35. The probability that an employee is promoted is P(M) = 0.22. The probability that an employee has both completed the training program and is promoted is P(TꓵM) = 0.14. We would like to look at the effect of the training program on those who has completed it. Find the probability that an employee is promoted if he/she has completed the training program.

Answer 1

1. For discrete probability distribution, P(X 5) = P(X = 5) + P(X < 5)

2. Bayes' Theorem: P(A | B) = P(A & B)/P(B)

P(employee is promoted if he/she has completed the training program), P(M | T) = P(an employee has both completed the training program and is promoted) / P(an employee has completed a training program)

= P(T M)/P(M)

= 0.14/0.35

= 0.4