Suppose that we have two events, A and 8, with PA) . .60. PrB)·.70, and na)·40.

Question

Suppose that we have two events, A and 8, with PA) . .60. PrB)·.70, and na)·40. a. Find P(A1 B) (to 4 decimals). b. Find pre A)(to 4 decimals). c. Are A and B independent? Why or why not? because PIA 1 B) is PTA) (Exercise 4.33Algorithmic)) Students taking the Graduate Management Admissions Test (GMAT) were asked about their undergraduate major and intent to pursue their MBA as a full-time or part-time student. A summary of their responses follows a. Develop a joint probability table for these data (to 3 decimals). b. Use the marginal probabilities of undergraduate major (Business, Engineering, or Other) to comment on which undergraduate major produces the most potential MBA students c· If a student itends to attend classes full-time in pursuit of an MBA degree, what is the probability that the student was an undergraduate Engineering major (to 3 decimals)? d. If a student was an undergraduate Business major, what is the probability that the student intends to attend classes full-time in pursuit of an MBA degree (to 3 decimals)? e Let A denote the event that student intends to attend classes full-time in pursuit of an MBA degree, and let B denote the event that the student was an undergraduate Business major. Are events A and B independent?

Explanation / Answer

WHEN A,B & INTERSECTION IS KNOWN
Given that, P(A) = 0.6 ,P(B) = 0.7 , P(A n B) = 0.40
a.
P( A|B) = P(A n B)/P(B) = 0.40/0.7 = 0.57142

b.
P(B|A) = P(A n B)/P(A) = 0.40/0.6 = 0.66667

c.
If A and B are not independent events because P(A|B) not equal to P(A)
P(A and B) = P(A) • P(B)
P (A or B) = P(A)+P(B) - P(A) • P(B)
0.40 ! = 0.6 * 0.7

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