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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

Respuesta :

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

Answer:

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

Step-by-step 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,

[tex]P(A|B)=\frac{P(A\bigcap B)}{P(B)}[/tex].

So, we have that,

[tex]P(Male|Type\ B)=\frac{P(Male\bigcap Type\ B)}{P(Type\ B)}\\\\P(Male|Type\ B)=\frac{48}{70}\\\\P(Male|Type\ B)=0.68[/tex]

[tex]P(Male\ Or\ TypeB)=P(Male)+P(Type\ B)-P(Male\bigcap TypeB)\\\\P(Male\ Or\ TypeB)=\dfrac{103}{200}+\dfrac{70}{200}-\dfrac{48}{200}\\\\P(Male\ Or\ TypeB)=0.52+0.35-0.24\\\\P(Male\ Or\ TypeB)=0.63[/tex]

Thus, we have that,

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

So, option C is correct.

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