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 ,$P(\frac{S}{A})$.

$P(\frac{S}{A})=\frac{P(S\cap A)}{P(A)}\\\\P(\frac{S}{A})=\frac{\frac{21}{100}}{\frac{36}{100}}\\\\P(\frac{S}{A})=\frac{21}{36}=\frac{7}{12}$

In terms of Percentage , Required Probability

  $=\frac{7}{12}\times 100\\\\=58.34$

= 58.34 %

 

Answer 2

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

Step-by-step 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" :

$P(S\mid A)=\frac{P(A\cap S)}{P(A)}\\\\P(S\mid A)=\frac{21}{36}\\\\P(S\mid A)=0.58\\\\P(S\mid A)=58\%$

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