Question

A two-way frequency table shows baldness in men over 45 and men under 45:

Under 45 Over 45 Total
Bald 24 16 40
Not Bald 36 24 60
60 40 100
Based on this data, are baldness and being over 45 independent events?

Answer 1

Yes, Based on this data, baldness and being over 45 are independent events, because P(bald | over 45) = P(bald).

Explanation:

The given data is as following:

Under 45 Over 45 Total

Bald : 24 16 40

Not Bald : 36 24 60

Total : 60 40 100

We should know that:

The events A and B are independent when If P(A∩B) = P(A) * Pr(B)

Using conditional probabilities this property can be written as:

P(A|B) = P(A∩B)/P(B) = P(A) * Pr(B)/ P(B) = P(A)

So, we will check baldness and being over 45 independent events.

From the given data:

1. P(man is bald) = 40/100 = 0.4

3. P(bald | over 45) = 16/40 = 0.4

So, P(man is bald) = P(bald | over 45) = 0.4

So, The events are independent.