Question

question
let ( s ) be the event that a randomly chosen store is having a sale. let ( m ) be the event that a randomly chosen store has marked up their prices in the last six months. identify the answer which expresses the following with correct notation: given that the store is having a sale, the probability that a randomly chosen store has marked up their prices in the last six months.

select the correct answer below:

( \bigcirc ) ( p(m) ) and ( p(s) )
( \bigcirc ) ( p(m|s) )
( \bigcirc ) ( p(s|m) )
( \bigcirc ) ( p(s \text{ and } m) )

Explanation:

We need to find the probability of event \( M \) (marked up prices) given that event \( S \) (having a sale) has occurred. The notation for conditional probability is \( P(A|B) \), which means the probability of \( A \) given \( B \). Here, \( A = M \) and \( B = S \), so the correct notation is \( P(M|S) \).

• \( P(M) \) AND \( P(S) \) is not conditional probability notation.
• \( P(S|M) \) is the probability of \( S \) given \( M \), which is the reverse of what we need.
• \( P(S \text{ AND } M) \) is the probability of both \( S \) and \( M \) occurring, not a conditional probability.

Answer:

\( P(M|S) \)