#### Answer

a. i. P(likes chocolate ice cream)=$\frac{207}{700}= 0.2957$
ii. P(women) =$ \frac{400}{700}$ = 0.5714
iii.P(likes vanilla ice cream| woman) = $\frac{143}{400}$=0.3575
iv. (man | likes chocolate ice cream) = $\frac{98}{207}$=0.4734
b. Men and vanilla ice cream are non mutually exclusive.
c. Not independent

#### Work Step by Step

b. Men and vanilla ice cream are non mutually exclusive.
P(men) ∩ P(vanilla ice cream ) = $\frac{79}{700}$
= 0.1129
Because P(men) ∩ P(vanilla ice cream )$ \ne 0$, thus it is non mutually exclusive.
c. P(women)= 0.5714, P(women|chocolate ice cream) = $\frac{109}{207}$ = 0.5265
P(women)$ \ne $P(women|chocolate ice cream), thus they are not independent events.