Given,
The data table of the gender and its type is shown in question tab.
Required
P(male or Type B)
P(Male| type B)
The value of P( male or Type B) is calculated as,
[tex]\begin{gathered} P\left(male\text{ }or\text{ }TypeB\right)\text{ =}\frac{65+38+12}{65+85+38+12} \\ =\frac{115}{200} \\ =\frac{57.5}{100} \\ =0.575 \end{gathered}[/tex]
The value of P(Male|Type B) is calculated as,
[tex]\begin{gathered} P(Male|Type\text{ B\rparen=}\frac{38}{50} \\ =\frac{76}{100} \\ =0.76 \end{gathered}[/tex]
Here, P( male or Type B) < P(Male|Type B) .
Hence, option (P( male or Type B) < P(Male|Type B) ) is correct.
