Independent events Problem set A Answers

P(both) = 0.27

Independent: P(both) = 0.15, product = 0.15

P(B) = 0.35

P(B) = \(\frac{2}{5}\) ≈ 0.400

1. (a) 0.6
2. (b) No: independence gives P(A ∩ B) = 0.1, not 0.

1. (a) \(\frac{13}{36}\) ≈ 0.361
2. (b) 52 times

1. (a) \(\frac{1}{8}\) ≈ 0.125
2. (b) \(\frac{1}{4}\) ≈ 0.250

1. (a) Only swim 30, both 15, only cycle 35, neither 40
2. (b) \(\frac{1}{3}\) ≈ 0.333
3. (c) \(\frac{3}{7}\) ≈ 0.429

1. (a) No: the king of hearts is both.
2. (b) Yes: P(H) × P(K) = 1/52 = P(H ∩ K).

0.65

P(B) = 0.55