At Thomas Jefferson High School, Students Are Heavily Involved in Extra-Curricular

At Thomas Jefferson High School, students are heavily involved in extra-curricular
activities. Suppose that a student is to be selected at random from the students at this
school. Let the events A, M, and S be defined as follows, with the probabilities
listed: $\mathrm { A } =$ a randomly selected student is active in the performing arts: $\mathrm { P } ( \mathrm { A } ) = 0.20$
$\mathrm { M } =$ a randomly selected student is active music: $\quad \mathrm { P } ( \mathrm { M } ) = 0.32$
$\mathrm { S } =$ a randomly selected student is active in sports:
$\mathrm { P } ( \mathrm { S } ) = 0.35$
Also
$$P ( A \cap M ) = 0.18 ; \quad P ( A \cap S ) = 0.07 ; \quad P ( M \mid S ) = 0.30$$
Calculate each of the following (show your work):
a) $P ( A \mid M )$
b) $P ( A \cup M )$
c) $P ( M \cap S )$