Country Club Activities At the Avonlea Country Club, 66%
of the members play bridge and swim, and 83%
play bridge. If a member is selected at random, find the probability that the member swims, given that the member plays bridge. Please round the final answer to 2
or 3
decimal places.

This problem can be solved using conditional probability. The goal is to find the probability that a member swims, given that the member plays bridge. 

Let:
- \( P(S) \) be the probability that a member swims.
- \( P(B) \) be the probability that a member plays bridge.
- \( P(S \cap B) \) be the probability that a member swims and plays bridge.

From the problem, we know:
- \( P(S \cap B) = 0.66 \) (66% of members play bridge and swim).
- \( P(B) = 0.83 \) (83% of members play bridge).

We need to calculate the conditional probability \( P(S|B) \), which is the probability that a member swims, given that the member plays bridge. The formula for conditional probability is:

\[
P(S|B) = \frac{P(S \cap B)}{P(B)}
\]

Substituting the known values:

\[
P(S|B) = \frac{0.66}{0.83}
\]

Now, let's compute this.

\[
P(S|B) \approx 0.795
\]

So, the probability that a member swims given that they play bridge is approximately **0.795** or **79.5%**.

Would you like further details on this, or do you have any other questions?

Here are 5 related questions you might want to explore:
1. What is the probability that a member swims but does not play bridge?
2. How would the solution change if 50% of members played both bridge and swam?
3. How is conditional probability applied in other real-life scenarios like medical testing?
4. Can you calculate the probability that a randomly selected member neither swims nor plays bridge?
5. How do you calculate joint probabilities when more than two activities are involved?

**Tip:** Conditional probability helps in understanding relationships between events when additional information is provided.

At the Avonlea Country Club, 66% of the members play bridge and swim, and 83% play bridge. If a member is selected at random, find the probability that the member swims, given that the member plays bridge. Please round the final answer to 2 or 3 decimal places.

Calculate the conditional probability that a member of Avonlea Country Club swims, given that they play bridge. With 66% of members playing both and 83% playing bridge, learn to apply the conditional probability formula P(A|B) = P(A ∩ B) / P(B). Suitable for Grades 10-12 students.

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