Question

suppose the data below represent, in thousands, the type of health insurance coverage of people by age. determine p(<18 years old) and p(<18 years old | no health insurance). are the events \<18 years old\ and
o health insurance\ independent?
<18
18 - 44
45 - 64

64

total
private health insurance
49,308
71,254
54,856
20,258
195,676
government health insurance
22,092
14,891
10,595
35,705
83,283
no health insurance
9,906
26,975
13,925
741
51,547
total
81,306
113,120
79,376
56,704
330,506
p(<18 years old) = 246
(round to three decimal places as needed.)
p(<18 years old | no health insurance) = 122
(round to three decimal places as needed.)

Explanation:

Step1: Calculate \(P(< 18\ years\ old)\)

The formula for probability is \(P(A)=\frac{n(A)}{n(S)}\), where \(n(A)\) is the number of elements in event \(A\) and \(n(S)\) is the total number of elements in the sample space.
Here, \(n(<18\ years\ old)=49308 + 22092+9906=81306\) and \(n(S) = 195676\)
So, \(P(<18\ years\ old)=\frac{81306}{195676}\approx0.416\)

Step2: Calculate \(P(<18\ years\ old|no\ health\ insurance)\)

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\)
Here, \(n(<18\ years\ old\cap no\ health\ insurance) = 9906\) and \(n(no\ health\ insurance)=51547\)
So, \(P(<18\ years\ old|no\ health\ insurance)=\frac{9906}{51547}\approx0.192\)

Answer:

\(P(<18\ years\ old)\approx0.416\), \(P(<18\ years\ old|no\ health\ insurance)\approx0.192\)