Musical styles other than rock and pop are becoming more popular. A survey of college students finds that 34% like country music, 32% like gospel music, and 12% like both.
What is the conditional probability (±0.01) that a student likes gospel music, given that he or she likes country music
To find the conditional probability that a student likes gospel music, given that they like country music, we need to use the formula for conditional probability:
P(A|B) = P(A and B) / P(B)
In this case, event A represents liking gospel music, and event B represents liking country music.
First, let's calculate P(A and B), which is the probability that a student likes both gospel music and country music. The given information tells us that 12% of the students like both genres. So, P(A and B) = 0.12.
Next, let's calculate P(B), which is the probability that a student likes country music. The survey tells us that 34% of the students like country music. So, P(B) = 0.34.
Now, we can use the formula to find the conditional probability:
P(A|B) = P(A and B) / P(B)
P(A|B) = 0.12 / 0.34
P(A|B) ≈ 0.35
Therefore, the conditional probability (±0.01) that a student likes gospel music, given that they like country music, is approximately 0.35, or 35%.