Question

The probability that a student at certain high school likes art is 36%. The probability that a student who likes art also likes science is 21%. Find the probability that a student chosen at random likes science given that he or she likes art. Round to the nearest tenth of a percent.

Answer 1

Answer: Probability that a student chosen at random likes science given that he or she likes art is 58%

Explanation:

Since we have given that

Probability that a student who likes art and science = 21%

Probability that a student who likes art = 36%

According to question,

we need to find the probability that a student chosen at random likes science given that he or she likes art.

So, we will use "Conditional Probability":

P(A) = 0.36

P(S ∩ A) = 0.21

`P(S\mid A)=(P(S\cap A))/(P(A))\\\\P(S\mid A)=(0.21)/(0.36)\\\\P(S\mid A)=0.58\\\\P(S\mid A)=58\%`

Hence, Probability that a student chosen at random likes science given that he or she likes art is 58%.