Statistics Question Addition Rule

Question

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).

3) P(G) =

4. Suppose P(H) = .25 , P(H or K) = .70, and events H and K are independent. Find P(K).

4) P(K) =

Answer 1

1 a) P(A^B) = 0 zero possibility of mutually exclusive events happening together

1 b) P(AvB) = .7 + .18 = .88

2 a) P(C^D) = .7 x .2 = .14

2 b) P(CvD) = .7 + .2 - .14 = .9-.14 = .76

3) P(G) = P(GvF) - P(F) = .7 - .25 = .45

4) P(K) =

Answer 2

1. Suppose P(A) = .70 , P(B) = .18 , and events A and B are mutually exclusive. Find…

a) P(A and B) = 0 (events that are mutually exclusive cannot occur at the same time)

b) P(A or B) = 0.70 + 0.18 = 0.88

2. Suppose P(C) = .70 , P(D) = .20 , and events C and D are independent. Find…

a) P(C and D) = 0.70 * 0.20 = 0.14

b) P(C or D) = 0.70 + 0.20 - 0.14 = 0.76

3. Suppose P(F) = .25 , P(F or G) = .70, and events F and G are mutually exclusive. Find P(G).

P(F or G) = P(F) + P(G) - P(F and G)

since mutually exclusive, P(F and G) = 0

P(F or G) = P(F) + P(G)

0.7 = 0.25 + P(G)

3) P(G) = 0.45

4. Suppose P(H) = .25 , P(H or K) = .70, and events H and K are independent. Find P(K).

P(H or K) = P(H) + P(K) - P(H and K)

0.70 = 0.25 + P(K) - P(H)*P(K)

0.70 = 0.25 + P(K) - 0.25*P(K)

0.70 = 0.25 + 0.75 * P(K)

0.55 = 0.75 * P(K)

4) P(K) = 0.73