Question

1. buffy is choosing people for her volleyball team in gym class. there are 14 girls and 18 boys to choose from, and she gets two selections. what is the probability she chooses a girl as her first selection, and then a girl as her second selection? $\frac{1}{14} \times \frac{1}{13}=\frac{1}{182}$ $\frac{14}{32} \times \frac{13}{31}=\frac{182}{992}=\frac{91}{496}$ $\frac{14}{32}+\frac{13}{31}=\frac{850}{992}=\frac{425}{496}$ $\frac{1}{14}+\frac{1}{13}=\frac{27}{182}$

Explanation:

Step1: Calculate total number of people

The total number of people is $14 + 18=32$.

Step2: Calculate probability of first - girl selection

The probability of choosing a girl first is $\frac{14}{32}$ since there are 14 girls out of 32 people.

Step3: Calculate probability of second - girl selection

After choosing a girl first, there are 13 girls left and 31 people left. So the probability of choosing a girl second is $\frac{13}{31}$.

Step4: Calculate combined probability

Since these are independent - like (sequential) events, we multiply the probabilities: $\frac{14}{32}\times\frac{13}{31}=\frac{182}{992}=\frac{91}{496}$.

Answer:

$\frac{14}{32}\times\frac{13}{31}=\frac{182}{992}=\frac{91}{496}$