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%

Step-by-step 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

$P(S\mid A)=\frac{P(S\cap A)}{P(A)}\\\\P(S\mid A)=\frac{0.21}{0.36}\\\\P(S\mid A)=0.58\\\\P(S\mid A)=58\%$

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