some randomly selected high school students were asked to name their favorite sport to watch. the table…
some randomly selected high school students were asked to name their favorite sport to watch. the table displays the distribution of results.\n| sport | football | basketball | baseball | soccer | none |\n| probability | 0.23 | 0.18 | 0.26 | 0.17 | 0.16 |\nwhat is the probability that a student chose football given that they like watching sports?\n0.16\n0.23\n0.27\n0.77
Answer
Explanation:
Step1: Find probability of liking sports
The probability of liking sports is the sum of probabilities of choosing football, basketball, baseball and soccer. So we calculate $P(\text{liking sports})=0.23 + 0.18+0.26 + 0.17=0.84$.
Step2: Calculate conditional - probability
The probability of choosing football given that a student likes watching sports is a conditional probability. The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. Here, event $A$ is choosing football and event $B$ is liking sports. Since choosing football implies liking sports, $P(A\cap B) = P(A)=0.23$ and $P(B)=0.84$. Then $P(\text{football}|\text{liking sports})=\frac{0.23}{0.84}\approx0.27$.
Answer:
0.27