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german
3 years ago
8

How many different outfits can be made from 3 shirts, 4 pants, 2 belts, and 2 hats?

Mathematics
1 answer:
Luda [366]3 years ago
6 0
How many different outfits can be made from 3 shirts, 4 pants, 2 belts, and 2 hats
11

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Answer:

P(B|A)=\frac{2}{7}

Step-by-step explanation:

The probability of P(B|A) can be read as the probability of event B occurring given event A. In this question, event A occurs when the chosen player is a girl. There are 7 girls on the soccer team. Event B occurs when the chose player plays defense. Since P(B|A) stipulates that event A already occurred, we want the probability of choosing a player who prefers defense from the 7 girls. There are 2 girls who prefer defense, hence P(B|A)=\boxed{\frac{2}{7}}.

<u>Alternative:</u>

For dependent events A and B, the conditional probability of event B occurring given A is given by:

P(B|A)=P(B\cap A)\div P(A)

P(B\cap A) indicates the intersection of P(B) and P(A). In this case, it is the probability that both events occur. Since there are 16 kids on the soccer team and only 2 are girls and prefer defense, P(B\cap A)=\frac{2}{16}=\frac{1}{8}. The probability of event A occurring (chosen player is a girl) is equal to the number of girls (7) divided by the number of kids on the team (16), hence P(A)=\frac{7}{16}.

Therefore, the probability of event B occurring, given event A occurred, is equal to:

P(B|A)=\frac{1}{8}\div \frac{7}{16},\\\\P(B|A)=\frac{1}{8}\cdot \frac{16}{7}=\boxed{\frac{2}{7}}

5 0
3 years ago
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