Homework SourseThe following twoway contingency table gives the breakdown o
The following two-way contingency table gives the breakdown of the population in a particular locale according to age and number of vehicular moving violations in the past three years:
A person is selected at random. Find the following probabilities.
A.The person is under 21.
B.The person has had at least two violations in the past three years.
C.The person has had at least two violations in the past three years, given that he is under 21.
D.The person is under 21, given that he has had at least two violations in the past three years.
E. Determine whether the events “the person is under 21” and “the person has had at least two violations in the past three years” are independent or not.
| Age | Violations | ||
|---|---|---|---|
| 0 | 1 | 2+ | |
| Under 21 | 0.04 | 0.06 | 0.02 |
| 21–40 | 0.25 | 0.16 | 0.01 |
| 41–60 | 0.23 | 0.10 | 0.02 |
| 60+ | 0.08 | 0.03 | 0.00 |
Solution
a)
P(under 21) = 0.04 + 0.06 + 0.02 = 0.12 [answer]
************
b)
P(2+) = 0.02+0.01+0.02+0.00 = 0.05 [answer]
***********
c)
P(2+|under 21) = P(2+ and under 21) / P(under 21) = 0.02 / 0.12
= 0.1666667 [answer]
*************
d)
P(under 21|2+) = P(2+ and under 21) / P(2+) = 0.02/0.05
= 0.40 [answer]
*****************
e)
As
P(under 21|2+) = 0.40 and
P(under 21) = 0.12 are not equal, then NO: THEY ARE NOT INDEPENDENT.
