Independent events Problem set B Answers

P(both) = 0.165

Not independent: P(both) = 0.15, product = 0.18

P(B) = 0.45

P(B) = \(\frac{2}{3}\) ≈ 0.667

1. (a) 0.58
2. (b) No: independence gives P(C ∩ D) = 0.12, not 0.

1. (a) \(\frac{7}{18}\) ≈ 0.389
2. (b) 42 times

1. (a) \(\frac{1}{8}\) ≈ 0.125
2. (b) \(\frac{11}{32}\) ≈ 0.344

1. (a) Only a car 45, both 25, only a bicycle 30, neither 60
2. (b) \(\frac{3}{8}\) ≈ 0.375
3. (c) \(\frac{3}{7}\) ≈ 0.429

1. (a) No: 6 is both.
2. (b) Yes: P(M) × P(E) = 1/6 = P(M ∩ E).

0.55

P(B) = 0.7