Answer
Let M denotes male and F denotes female, S denotes adults prefer watching sports, O denotes adults watching opera, and N denotes the total number of adults.
Total number of male = $96+24 = 120$
Total number of female = $45+85 =130$
i. P(O) = $\frac{24+85}{250}$
$=\frac{109}{250}$
$=0.436$
ii. P(M) $= \frac{96+24}{N}$
$=\frac{120}{250}$
=0.48
iii. P(S|F) = $\frac{45}{250}$
=0.18
iv. P(M|S)= $\frac{96}{250}$
=0.384
v.$P( F∩O)$ = $\frac{85}{250}$
=0.34
vi, $P(S U M)$ = $\frac{96+45+24}{250}$
=0.66
b. $P(F)$ = $\frac{130}{250}$
=0.52
$P(S) = \frac{141}{250}$
=0.564
$P(S ∩ F) = \frac{45}{250}$
=0.18
$P(S)+P(F) \ne P(S ∩ F)$
The events female and prefers watching sports are not independent. $P(S ∩ F)\ne 0 $ , therefore they are not mutually exclusive.
Work Step by Step
see above
