Question
On a track and field team, 8% of the members run only long-distance, 32% compete only in field events, and 12% are sprinters only. Find the probability that a randomly chosen team member runs only long-distance or competes only in field events.
Answers
GPT-4o mini
To find the probability that a randomly chosen team member either runs only long-distance or competes only in field events, we can use the principle of addition for probabilities.
Let:
- \( P(\text{long-distance}) \) = Probability that a member runs only long-distance = 8% = 0.08
- \( P(\text{field events}) \) = Probability that a member competes only in field events = 32% = 0.32
Since these two events (running long-distance and competing in field events) are mutually exclusive (a member cannot be both), we can simply add the probabilities:
\[
P(\text{long-distance or field events}) = P(\text{long-distance}) + P(\text{field events})
\]
Substituting in the values:
\[
P(\text{long-distance or field events}) = 0.08 + 0.32 = 0.40
\]
Thus, the probability that a randomly chosen team member runs only long-distance or competes only in field events is \( \boxed{0.40} \) or 40%.
Let:
- \( P(\text{long-distance}) \) = Probability that a member runs only long-distance = 8% = 0.08
- \( P(\text{field events}) \) = Probability that a member competes only in field events = 32% = 0.32
Since these two events (running long-distance and competing in field events) are mutually exclusive (a member cannot be both), we can simply add the probabilities:
\[
P(\text{long-distance or field events}) = P(\text{long-distance}) + P(\text{field events})
\]
Substituting in the values:
\[
P(\text{long-distance or field events}) = 0.08 + 0.32 = 0.40
\]
Thus, the probability that a randomly chosen team member runs only long-distance or competes only in field events is \( \boxed{0.40} \) or 40%.