Question

some randomly selected high school students were asked to name their favorite sport to watch. the table displays the distribution of results. what is the probability that a student chose football given that they like watching sports? 0.16 0.23 0.27 0.77

Explanation:

Step1: Calculate the probability of liking watching sports

The probability of liking watching sports is \(1 - P(\text{None})\).
\(P(\text{like sports})=1 - 0.16=0.84\)

Step2: Use the formula for conditional probability

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). Here, \(A\) is the event of choosing football and \(B\) is the event of liking watching sports. Since \(P(A\cap B) = P(\text{Football})\) (if a student chose football, they like sports), \(P(\text{Football}) = 0.23\) and \(P(B)=0.84\).
\(P(\text{Football}|\text{like sports})=\frac{0.23}{0.84}\approx0.27\)

Answer:

\(0.27\)