In a management trainee program at Claremont Enterprises, 80 percent of the trainees are female and 20 percent male. Ninety percent of the females attended college, and 78 percent of the males attended college.

a. A management trainee is selected at random. What is the probability that the person selected is a female who did not attend college?

b. Are gender and attending college independent? Why?

c. Construct a tree diagram showing all the probabilities, conditional probabilities, and joint probabilities.

d. Do the joint probabilities total 1.00? Why?

Answer: a. 8% ; b. Not independent; c. See tree diagram; d. Yes

Step-by-step explanation:

a. Let F = Females

M = Males

C = Those that attend college

P(F) = 80% = 0.8

P(M) = 20% = 0.2

P(C/F) = 90% = 0.9

P(C/M) = 78% = 0.78

If 90% of the females go to college, it means that 10% don't go to college.

We then use the multiplication rule and we'll get:

= 80% × 10%

= 0.8 × 0.1

= 0.08

= 8%

b. An independent event is one that the occurence of one event doesn't affect the other event from happening. However, this is not independent as the occurence of the events affect each other.

c. See attachment

The joint probability on the tree diagram will be:

= 0.72 + 0.08 + 0.156 + 0.044

= 1.00

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