Question

The venn diagram represents the number of people at the gym that are signed up for yoga or aerobics class.

What is the probability of picking someone that has signed up for yoga
yoga:68
both:24
aerobics:89
575

Answer 1

To find the probability of picking someone who is signed up for yoga, we need to determine the total number of people who have signed up for yoga and then divide that by the total number of people surveyed.

**Step 1: Calculate the total number of people who are signed up for yoga.**
- The number of people signed up for yoga only: 68
- The number of people signed up for both classes (yoga and aerobics): 24

Thus, the total number of people signed up for yoga is:
\[
68 + 24 = 92
\]

**Step 2: Determine the total number of people surveyed.**
The total number of people is given as 575.

**Step 3: Calculate the probability.**
The probability \(P\) of selecting someone who is signed up for yoga is given by the formula:
\[
P(\text{Yoga}) = \frac{\text{Number of people signed up for yoga}}{\text{Total number of people}}
\]
Plugging in the values:
\[
P(\text{Yoga}) = \frac{92}{575}
\]

**Step 4: Calculate the probability.**
Now, we can compute this fraction:
\[
P(\text{Yoga}) \approx 0.160
\]

Thus, the probability of picking someone who has signed up for yoga is approximately **0.160** or **16.0%**.