Answer:
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.
Answer:
Yes, P(bald ∩ over 45) = P(bald) ⋅ P(over 45)
Step-by-step explanation:
This might be right.
If it is, please say.
