Exhibit 4-1 You are given the following information on Events A, B, C, and D. P(

Question

Exhibit 4-1 You are given the following information on Events A, B, C, and D. P(A) = .3, P(B) = .2, P(C) = .1, PAS D)-6, PCA nd) = .02, P(A | B) = .4, PanD) = .02 20. Refer to Exhibit 4-1, compute P(D) a. 0.23 b. 0.32 c. 0.4 d. 0.6 Refer to Exhibit 4-1, compute P(A | C) a. 0.03 b. 0.04 c. 0.23 d. 0.2 21. Refer to Exhibit 4-1, compute P(AnB) a. 0.06 b. 0.08 c. 0.23 d. 0.4 22. Refer to Exhibit 4-1, are A and B mutually exclusive? a. Yes b. No c. Maybe d. None of the above 23. Refer to Exhibit 4-1, are A and C independent? a. Yes b. No c. Maybe d None of the above 24.

Explanation / Answer

P(A) = 0.3 P(B) = 0.2 P(C) = 0.1

P(A U D) = 0.6 P(A C) = 0.02

P(A|B) = 0.4 P(A D) = 0.02

20. P(D) = P(A U D) + P(A D) - P(A)

= 0.6 + 0.02 - 0.3

= 0.32.

21. P(A|C) = P(A C) / P(C)

= 0.02 / 0.1

= 0.2.

22. P(A B) = P(A|B) P(B)

= 0.4 * 0.2

= 0.08.

23. Since P(A B) is not equal to 0, A and B are NOT mutually exclusive.

The answer is NO.

24. Since P(A) and P(A|C) are not equal, A and C are NOT independent.

The answer is NO.

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