at kennedy high school, the probability of a student playing in the band is 0.15. the probability of a…

at kennedy high school, the probability of a student playing in the band is 0.15. the probability of a student playing in the band and playing on the football team is 0.03. given that a student at kennedy plays in the band, what is the probability that they play on the football team?\na. 0.03\nb. 0.12\nc. 0.15\nd. 0.18\ne. 0.20

at kennedy high school, the probability of a student playing in the band is 0.15. the probability of a student playing in the band and playing on the football team is 0.03. given that a student at kennedy plays in the band, what is the probability that they play on the football team?\na. 0.03\nb. 0.12\nc. 0.15\nd. 0.18\ne. 0.20

Answer

Answer:

E. 0.20

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. Let $A$ be the event of playing on the football team and $B$ be the event of playing in the band.

Step2: Identify given probabilities

We are given that $P(B) = 0.15$ (probability of playing in the band) and $P(A\cap B)=0.03$ (probability of playing in the band and on the football team).

Step3: Calculate the conditional probability

Substitute the values into the formula: $P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{0.03}{0.15}= 0.20$.