1. Suppose P(A) = .70, P(B) = .18, and events A and B are mutually exclusive. Find
a) P(A and B)
b) P(A or B)
2. Suppose P(C) = .70, P(D) = .20, and events C and D are independent. Find
a) P(C and D)
b) P(C or D)
3. Suppose P(F) = .25, P(F or G) = .70, and events F and G are mutually exclusive. Find P(G).
4. Suppose P(H) = .25, P(H or K) = .70, and events H and K are independent. Find P(K).
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1.
a) Since events A and B are mutually exclusive, P(A and B) = 0.
b) P(A or B) = P(A) + P(B) = 0.70 + 0.18 = 0.88.
2.
a) Since events C and D are independent, P(C and D) = P(C) * P(D) = 0.70 * 0.20 = 0.14.
b) P(C or D) = P(C) + P(D) - P(C and D) = 0.70 + 0.20 - 0.14 = 0.76.
3. Since events F and G are mutually exclusive, P(F or G) = P(F) + P(G) = 0.25 + P(G) = 0.70.
Solving for P(G):
0.25 + P(G) = 0.70
P(G) = 0.70 - 0.25
P(G) = 0.45.
4. Since events H and K are independent, P(H or K) = P(H) + P(K) - P(H and K) = 0.25 + P(K) - 0.
0.70 = 0.25 + P(K)
P(K) = 0.70 - 0.25
P(K) = 0.45.
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