At a picnic, two teams of kids played a soccer game, after which one player's name...

At a picnic, two teams of kids played a soccer game, after which one player's name was randomly chosen to win a prize. There are 22 kids in total. The winning team in the soccer game consists of 8 girls and 3 boys and the losing team consists of 4 girls and 7 boys. Given that the prize winner is a boy, what is the probability that he also comes from the winning soccer team?

Hint: Let E and F be events in a sample space S with P(F) > 0. The conditional probability of E given F is P(E|F) = P(E∩F) / P(F) = n(E∩F) / n(F)

Solutions

Expert Solution

Solution:

Given: There are 22 kids in total. The winning team in the soccer game consists of 8 girls and 3 boys and the losing team consists of 4 girls and 7 boys.

	Girls	Boys	Total
winning soccer team	8	3	11
Losing soccer team	4	7	11
Total	12	10	22

We have to find:

P( prize winner comes from the winning soccer team given that he is a boy) = ...........?

that is find:

P( W | B ) =............?

orchestra answered 1 year ago

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