Final answer:
To calculate the probability that someone likes art, assuming they also like math, we need to determine the probability of liking art given that they like math. This can be calculated using conditional probability.
Step-by-step explanation:
To calculate the probability that someone likes art, assuming they also like math, we need to determine the probability of liking art given that they like math. This can be represented as P(art|math). In order to calculate this probability, we need to know the probability of liking both art and math (P(art ∩ math)) and the probability of liking math (P(math)). The formula we can use is:
P(art|math) = P(art ∩ math) / P(math)
For example, if 25% of people like both art and math (P(art ∩ math) = 0.25) and 50% of people like math (P(math) = 0.5), then the probability of liking art given that they like math would be:
P(art|math) = 0.25 / 0.5 = 0.5
So the probability that someone likes art, assuming they also like math, is 50%.