Find the probability

Question

According to the Census Bureau, 20.3% of households are headed by someone age 65 or older. Of these households, the probability that the household income is less than $25,000 is .307. Of households that are headed by someone less than 65 years old, the probability that the household income is less than $25,000 is .225. Find the probability that

 

a) a household with income less than $25,000 is headed by someone 65 years or older

b) a household with income $25,000 or higher is headed by someone younger than age 65

Answer 1

 

a)  20.3%= .203;     .203x.307=.062

b) .797x.775=.618

Answer 2

Hi Jean,

 

If 20.3% of households are headed by someone 65 or older, then 79.7% are headed by someone younger than 65.

 

65+ < 25,000 = .307

65+ > 25,000 = .693

 

0-64 < 25,000 = .225

0-64 > 25,000 = .775

 

Now we have all that laid out, we can find the probabilities by multiplying them together, as they are independent events.

 

a) .203 x .307 = .062 (6.2%)

 

b) .797 x .775 = .617 (62%)