In: Statistics and Probability
a.
The marginal probabilities are calculated as below.
Age | Health Insurance Yes | Health Insurance No | Total |
18-34 | 0.375 | 0.085 | 0.46 |
35 and up | 0.475 | 0.065 | 0.54 |
Total | 0.85 | 0.15 | 1 |
Probability that she/he does not have health insurance coverage given randomly selected individual is 35 and older,
= Probability that she/he does not have health insurance coverage and individual is 35 and older / Probability that randomly selected individual is 35 and older
= 0.065 / 0.54
= 0.1203704
b.
Probability that she/he does not have health insurance coverage and individual is 35 and older
= P(Health Insurance No AND Age 35 and up) = 0.065
Now,
P(Health Insurance No) = 0.15
P(Age 35 and up) = 0.54
P(Health Insurance No) * P(Age 35 and up) = 0.15 * 0.54 = 0.081
Since,
P(Health Insurance No AND Age 35 and up) P(Health Insurance No) * P(Age 35 and up)
age and health insurance coverage (or lack of coverage) are not independent.
c.
Probability that "at least one" of them does not have health insurance = 1 - Probability that all of them have health insurance
= 1 - 0.85 * 0.85
= 0.2775