Questions: Use the completed contingency table to find the probability that a cyclist prefers a lake path, given that they are female. Express your answer as a decimal rounded to two decimal places.

Solution Steps

Let:

• \( A \): the event that a cyclist prefers a lake path.
• \( B \): the event that a cyclist is female.

We want to find the conditional probability \( P(A|B) \).

From the contingency table, we have:

• The number of females who prefer the lake path: \( P(A \cap B) = 45 \)
• The total number of females: \( P(B) = 110 \)

Using the formula for conditional probability:

\[ P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{45}{110} \]

Calculating the fraction:

\[ P(A|B) = \frac{45}{110} = 0.4090909091 \]

Rounding this to two decimal places gives:

\[ P(A|B) \approx 0.41 \]

Final Answer