Question

A group of people were given a personality test to determine if they were type a or type b. The results are in the table shown below.

Male and type a=55
Male and type b=48
Female and type a=75
Female and type b=22
Compare p(male or type b) with p(male | type b).
A. P(male or type b) > p(male | type b)
B. P(male or type b) = p(male | type b)
C. P(male or type b) < p(male | type b)
D. There is not enough information.
I think it is c. Because I got 0.63 for P(make or type b) and 0.69 for p(male | type b). Am i right? Pls help

Answer 1

yes u are right the information on the table is not much so u have to use what you have it is correct

Answer 2

C. P(Male\ Or\ TypeB) < P(Male|Type\ B)

Explanation:

We are given,

The table representing the gender with the personality type is,

Type A Type B Total

Male 55 48 103

Female 75 22 97

Total 130 70 200

The conditional probability of event A given that event B is P(A|B), where,

`P(A|B)=(P(A\bigcap B))/(P(B))`.

So, we have that,

`P(Male|Type\ B)=(P(Male\bigcap Type\ B))/(P(Type\ B))\\\\P(Male|Type\ B)=(48)/(70)\\\\P(Male|Type\ B)=0.68`

`P(Male\ Or\ TypeB)=P(Male)+P(Type\ B)-P(Male\bigcap TypeB)\\\\P(Male\ Or\ TypeB)=(103)/(200)+(70)/(200)-(48)/(200)\\\\P(Male\ Or\ TypeB)=0.52+0.35-0.24\\\\P(Male\ Or\ TypeB)=0.63`

Thus, we have that,

0.63 = P(Male\ Or\ TypeB) < P(Male|Type\ B) = 0.68

So, option C is correct.