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?

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

Step-by-step 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.