Peter and Lucy

In a group of 3 boys and 4 girls, two players are drawn to play a game. Among the girls is Lucy, and among the boys is Petr (both are the only ones with that name). The first one drawn will be the captain, the second the helmsman. What is the probability that:
a) The captain will be a boy and the helmsman will be a girl.
b) Will Peter and Lucy be among the winners?
c) If a boy became the captain, was it Peter?

Correct answer:

p₁ =  0.2857
p₂ =  0.0238
p₃ =  0.1429

Step-by-step explanation:

$p_1=\frac{3}{3+4}\cdot \frac{4}{3+4-1}=\frac{2}{7}=0.2857$

$p_2=\frac{1}{3+4}\cdot \frac{1}{3+4-1}=\frac{1}{42}=0.0238$

$p_3=\frac{3}{3+4}\cdot \frac{1}{3}=\frac{1}{7}=0.1429$

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