Question

Use the two way table below to answer the question given.

Favor Do not favor No opinion
Male 20 15 17
Female 18 12 7
Are the events 'male' and 'favor independent?

Answer 1

Since
`P(A)P(B) \\eq P(A \cap B)`, these two events are not independent.

Explanation:

Independent events:

Two events, A and B, are independent if:

`P(A \cap B) = P(A)*P(B)`

In this question:

Event A: Male

Event B: Independent

Probability of male:

20 + 15 + 17 = 52 out of (20 + 15 + 17 + 18 + 12 + 7) = 89.

So

`P(A) = (52)/(89)`

Probability of favoring independent:

20 + 18 = 38 out of 89. So

`P(B) = (38)/(89)`

Probability of male and favoring independent:

20 out of 89. So

`P(A \cap B) = (20)/(89)`

Test if they are independent:

`P(A)P(B) = (52)/(89)*(38)/(89) = (52*38)/(89*89) = 0.24946`

`P(A \cap B) = (20)/(89) = 0.22472`

Since
`P(A)P(B) \\eq P(A \cap B)`, these two events are not independent.