Respuesta :
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 =[tex]P(A)[/tex] = 36%
Probability that a student who likes art also likes science= [tex]P(A\cap S)[/tex] = 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" :
[tex]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\%[/tex]
Hence, Probability that a student chose at random likes science given that he or she likes art is 58%.
Answer with explanation:
A= Art
S= Science
P(A)= 36%
P (A ∩ S)=21%
We have to find ,[tex]P(\frac{S}{A})[/tex].
[tex]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}[/tex]
In terms of Percentage , Required Probability
[tex]=\frac{7}{12}\times 100\\\\=58.34[/tex]
= 58.34 %
