Question

note: remember to simplify fractions when necessary.
question
find the probability that a randomly chosen person takes public transit to work given that the person does not support the environmental bill.

people	drive to work	walk to work	public transit to work	total
do not support bill	20	3	10	33
total	25	33	30	88

give your answer as a fraction.
provide your answer below:

Explanation:

Step1: Identify relevant counts

We need the number of people who do not support the bill and take public transit (10) and the number of people who do not support the bill (33).

Step2: Apply conditional probability formula

The formula for conditional probability \( P(A|B) = \frac{P(A \cap B)}{P(B)} \). In terms of counts, this is \( \frac{\text{Count}(A \cap B)}{\text{Count}(B)} \). Here, \( A \) is "takes public transit" and \( B \) is "does not support the bill". So we calculate \( \frac{10}{33} \) (10 and 33 have no common factors other than 1, so it's already simplified).

Answer:

\(\frac{10}{33}\)