Answer
a. i. P(man) = $\frac{300}{600}$ = 0.5
ii. P(No) = $\frac{168}{600}$ = 0.28
iii. (Yes | woman ) = $\frac{106}{300}$ = 0.3533
iv. (man | no opinion) = $\frac{58}{128}$ = 0.4531
b. They are not mutually exclusive.
c. Not independent.
Work Step by Step
b. They are not mutually exclusive.
P(men) ∩ P(yes) = $\frac{74}{600}$ =$ 0.1233\ne 0$, therefore they are not mutually exclusive.
c. P(men) = 0.5
P(men|no) = $\frac{168}{292}$ = 0.5753
$P(men)\ne P(men|no)$ , therefore they are not independent.
