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:


Male Female
Type A 55 75
Type B 48 22


Compare P(Male or Type B) with P(Male | Type B).

Answers:
P(Male or Type B) > P(Male | Type B)
P(Male or Type B) = P(Male | Type B)
P(Male or Type B) < P(Male | Type B)
There is not enough information.

I need this fast, thanks!

Answer 1

Judging by the data set, there appears to be 200 participants: (103 males and 97 females)

P(Male or Type B): (103/200) + (70/200) which makes the P(Male or Type B) = 0.865

FORMULA: (Male|Type B) = P(Type B and Male) / P(Type B)

P(Type B and Male): (70/200)(103/200) = 0.18025

P(Type B): 70/200 = 0.35

Now that we know these 2 values, we plug them into the formula

P(Male|Type B): 0.18025 / 0.35 = 0.515

0.865 > 0.515 therefore P(Male or Type B) > P(Male|Type B)