Question

What is the probability that someone likes art, assuming they also like math?

a) 25%
b) 50%
c) 75%
d) 100%

Answer 1

The probability that someone likes art, assuming they also like math, is b) 50%.

Step-by-step explanation:

Understanding the probability of liking art given a liking for math involves considering the relationship between the two preferences. Let's denote the probability of liking art as P(A) and the probability of liking math as P(M). The conditional probability of liking art given a liking for math is represented as P(A | M).

In this case, if someone likes math (P(M) = 100%, as it is given), the probability of liking art is the conditional probability P(A | M). A conditional probability is calculated using the formula:

`\[ P(A | M) = (P(A \cap M))/(P(M)) \]`

Given that P(M) = 100%, the formula simplifies to
`\( P(A | M) = P(A \cap M) \)`. This means the probability of liking art and math is the same as the probability of liking math.

Therefore, the answer is 50% (option b), as the probability of liking art, assuming a liking for math, is 50%. This result is based on the assumption that liking math implies liking art in all cases, making the probability distribution between the two preferences equal.

The question is complete.