Question

in a certain geometry class of 32 students 11 of them play volleyball an 14 play tennis. there are 12 students who play neither sports. what is the probability that a student chosen randomly from the class plays volleyball or tennis? round to the nearest thousand

Answer 1

To find the probability that a student chosen randomly from the class plays volleyball or tennis, we can use the principle of inclusion-exclusion.

1. **Total number of students in the class**: 32
2. **Number of students who play neither sport**: 12
3. **Number of students who play volleyball**: 11
4. **Number of students who play tennis**: 14

First, we can find the number of students who play either volleyball or tennis (or both) by first calculating how many play either sport.

### Step 1: Calculate the number of students who play at least one of the sports.

The number of students who play at least one sport is the total number of students minus those who play neither:
\[
\text{Students who play at least one sport} = \text{Total Students} - \text{Students who play neither}
\]
\[
= 32 - 12 = 20
\]

### Step 2: Calculate the probability.

Now, we can find the probability \( P \) that a randomly chosen student from the class plays either volleyball or tennis:
\[
P(\text{plays volleyball or tennis}) = \frac{\text{Number of students who play at least one sport}}{\text{Total number of students}}
\]
\[
= \frac{20}{32} = \frac{5}{8}
\]

### Step 3: Convert to decimal and round.

Now we convert \( \frac{5}{8} \) to a decimal:
\[
\frac{5}{8} = 0.625
\]

Rounding to the nearest thousandth:
\[
P \approx 0.625
\]

So, the probability that a student chosen randomly from the class plays volleyball or tennis is **0.625** when rounded to the nearest thousandth.