Question

According to a 2017 Census Bureau survey, 12.6% of Americans are receiving Food Stamp assistance from the government, and 10.5% of Americans have no health insurance. Further, 7.7% of Americans fall into both categories. Using these rates, answer the following: (a) Are receiving Food Stamps and having no health insurance disjoint events? Explain. (b) What percent of Americans are receiving Food Stamps, but have health insurance? (c) What percent of Americans are receiving Food Stamps or have no health insurance? (d) What percent of Americans are not receiving Food Stamps and have health insurance? (e) Is the event of some American receiving Food Stamps independent of the event of not having health insurance?

Answer 1

Proportion of food stamp, P(A) = 0.126

Proportion of no health insurance, P(B) = 0.105

Proportion of both, P(A and B) = 0.077

a)

No, they are not disjoint events.

For disjoint event P(A and B) should be zero. This is not true in this case. so, they are not disjoint.

b)

Percent of Americans that are receiving Food Stamps, but have health insurance, P(A n B') =

= P(A) - P(A and B)

= 0.126 - 0.077

= 0.049 = 4.9%

c)

Percent of Americans are receiving Food Stamps or have no health insurance, P(A or B)

= P(A) +P(B) - P(A and B)

= 0.126 + 0.105 - 0.077

= 0.154 = 15.4%

d)

percent of Americans are not receiving Food Stamps and have health insurance, P(A' and B) =

= P(B) - P(A and B)

= 0.105 - 0.077

= 0.028 = 2.8%

e)

No, they are not independent.

for independent event, P(A and B) = P(A)*P(B)

As this is not true. so they are not independent.