Question

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

Answer 1

Answer:

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

Step-by-step 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

$P(A) = \frac{52}{89}$

Probability of favoring independent:

20 + 18 = 38 out of 89. So

$P(B) = \frac{38}{89}$

Probability of male and favoring independent:

20 out of 89. So

$P(A \cap B) = \frac{20}{89}$

Test if they are independent:

$P(A)P(B) = \frac{52}{89}*\frac{38}{89} = \frac{52*38}{89*89} = 0.24946$

$P(A \cap B) = \frac{20}{89} = 0.22472$

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