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?

Explanation:

Step1: Calculate \(P(\text{<18 years old})\)

The total number of people is \(203,573\). The number of people \(<18\) years old is \(49,462\). So \(P(\text{<18 years old})=\frac{49462}{203573}\approx0.243\)

Step2: Calculate \(P(\text{no health insurance})\)

The number of people with no health insurance is \(49,314\). So \(P(\text{no health insurance})=\frac{49314}{203573}\approx0.242\)

Step3: Calculate \(P(\text{<18 years old and no health insurance})\)

The number of people \(<18\) years old and with no health insurance is \(9,598\). So \(P(\text{<18 years old and no health insurance})=\frac{9598}{203573}\approx0.047\)

Step4: Check for independence

Two events \(A\) and \(B\) are independent if \(P(A\cap B)=P(A)\times P(B)\)
\(P(A)\times P(B)=0.243\times0.242 = 0.059\)
Since \(0.047
eq0.059\) (the values are not equal considering the rounding), the events are not independent

Answer:

No