The probability that a student takes art, given that the student takes music is 10.8%
In probability, we say two events are independent if knowing one event occurred doesn't change the probability of the other event.
For example, the probability that a fair coin shows "heads" after being flipped is 1/21/21, slash, 2. What if we knew the day was Tuesday? Does this change the probability of getting "heads?" Of course not. The probability of getting "heads," given that it's a Tuesday, is still 1/21/21, slash, 2. So the result of a coin flip and the day being Tuesday are independent events; knowing it was a Tuesday didn't change the probability of getting "heads."
Two events, A and B, are independent if
P(A ∣ B)=P(A)
P(A).P(B) = P(A ∩ B)
In the given question there are independent events.
Given:-
P(A) = Student takes both art and music = 0.9
P(B) = Student takes music = 0.12
P(A ∩ B) = student takes art, given that the student takes music
Thus by using the formula we get,
P(A ∩ B) = 0.9 x 0.12 = 0.108 = 10.8%
The probability that a student takes art, given that the student takes music is 10.8%
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