Question

let ( d ) be the event that a randomly chosen person has seen a dermatologist. let ( s ) be the event that a randomly chosen person has had surgery for skin cancer. identify the answer which expresses the following with correct notation: the probability that a randomly chosen person has had surgery for skin cancer, given that the person has seen a dermatologist.

select the correct answer below:

• ( p(d|s) )
• ( p(d \text{ and } s) )
• ( p(s) \text{ and } p(d) )
• ( p(s|d) )

Explanation:

Conditional probability notation \( P(A|B) \) means the probability of event \( A \) given that event \( B \) has occurred. Here, the event we're interested in (surgery for skin cancer, \( S \)) is given the condition (seen a dermatologist, \( D \)). So we use \( P(S|D) \). Other options: \( P(D|S) \) is \( D \) given \( S \), \( P(D \text{ AND } S) \) is joint probability, \( P(S) \text{ AND } P(D) \) is not conditional notation.

Answer:

\( P(S|D) \) (the option with \( P(S|D) \))