Question

A group of people were given a personality test to determine if they were type a or type B. The results are shown in the table below:…Compare P(Male or Type B) with P(Male | Type B)

Answer 1

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,

$\begin{gathered} P\left(male\text{ }or\text{ }TypeB\right)\text{ =}\frac{65+38+12}{65+85+38+12} \\ =\frac{115}{200} \\ =\frac{57.5}{100} \\ =0.575 \end{gathered}$

The value of P(Male|Type B) is calculated as,

$\begin{gathered} P(Male|Type\text{ B\rparen=}\frac{38}{50} \\ =\frac{76}{100} \\ =0.76 \end{gathered}$

Here, P( male or Type B) < P(Male|Type B) .

Hence, option (P( male or Type B) < P(Male|Type B) ) is correct.