Question

Drink
Sport
Skiing Snowboarding Total
Tea 27 32 59
Hot Cocoa 34 46 80
Total 61 78 139
43%

P(A|B)=n(A and B)n(B)=3480≈

Answer 1

To find the conditional probability \( P(A|B) \), where:

- \( A \) is the event that a person drinks Tea.
- \( B \) is the event that a person participates in Skiing.

Given the table, we have:

- Total number of people who drink Tea and Skiing (A and B): 27
- Total number of people who Ski: 61 (this is \( n(B) \))

Thus, we can calculate the conditional probability \( P(A|B) \):

\[
P(A|B) = \frac{n(A \text{ and } B)}{n(B)} = \frac{27}{61}
\]

Now, calculating \( \frac{27}{61} \):

\[
P(A|B) \approx 0.4426 \quad (\text{or approximately } 44.26\%)
\]

So, \( P(A|B) \) is about \( 0.4426 \). If you need it rounded or expressed differently, please let me know!