Question

You are given the following information on Events A, B, C, and D.

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P(A) = 0.4 P(A ? D) = 0.6

P(B) = 0.2 P(A?B) = 0.3

P(C) = 0.1 P(A ? C) = 0.04

P(A ? D) = 0 .03

a. Compute P(D).

b. Compute P(A ? B).

c. Compute P(A?C).

d. Compute the probability of the complement of C.

e. Are A and B mutually exclusive? Explain your answer.

f. Are A and B independent? Explain your answer.

g. Are A and C mutually exclusive? Explain your answer.

h. Are A and C independent? Explain your answer.

Here are the answers I found but I need to know HOW they got them. ANswers are useless without the work shown eh?

Answers:

a. 0.23

b. 0.06

c. 0.4

d. 0.9

e. No, P(A?B) ? 0

f. No, P(A?B) ?P(A)

g. No, P(A ? C) ? 0

h. Yes, P(A?C) = P(A)

Answer 1

a.
P(A) = 0.4
P(A or D) = 0.6
P(A and D) = 0.03
P(A or D) = P(A) + P(D) - P(A and D)
0.6 = 0.4 + P(D) - 0.03
P(D) = 0.23

b.
P(A | B) = P(A and B) / P(B)
0.3 = P(A and B) / 0.2
P(A and B) = 0.03 * 0.2
P(A and B) = 0.06

c.
P(A | C) = P(A and C) / P(C)
P(A | C) = 0.04 / 0.1
P(A | C) = 0.4

d.
P(not C) = 1 - P(C)
P(not C) = 1 - 0.1
P(not C) = 0.9