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 with explanation:

A= Art

S= Science

P(A)= 36%

P (A ∩ S)=21%

We have to find ,
`P((S)/(A))`.

`P((S)/(A))=(P(S\cap A))/(P(A))\\\\P((S)/(A))=((21)/(100))/((36)/(100))\\\\P((S)/(A))=(21)/(36)=(7)/(12)`

In terms of Percentage , Required Probability

`=(7)/(12)* 100\\\\=58.34`

= 58.34 %

Answer 2

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

Explanation:

Since we have given that

Probability that a student at certain high school likes art =
`P(A)` = 36%

Probability that a student who likes art also likes science=
`P(A\cap S)` = 21%

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

As we know the formula for "Conditional Probability" :

`P(S\mid A)=(P(A\cap S))/(P(A))\\\\P(S\mid A)=(21)/(36)\\\\P(S\mid A)=0.58\\\\P(S\mid A)=58\%`

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