An automobile company has 6,500 dealers who are polled to find out their annual

Question

An automobile company has 6,500 dealers who are polled to find out their annual incomes as well as their age. The number of dealers in each category are given below:
Incomes (dollars) Dealers under 40 Dealers 40 and above Total

Under 100,000 1,500 1,500 3,000

100,000 and over 1,000 2,500 3,500

Total 2,500 4,000 6,500

What is the probability that a randomly chosen dealer will:
a) Have an income under $100,000...?
b) Will have an income under $100,000, given that he or she is under 40...?
c) Be age 40 and above, given they have an income of $100,000 and over...?

Explanation / Answer

the table is given as follows

age under 40 age 40 and above total

income under 100,000 1500 1500 3000

income 100,000 and above 1000 2500 3500

total 2500 4000 6500

a)the probability that a randomly chosen dealer wll have an income under $100,000

is total number of dealers with income under $100,000/6500=3000/6500=0.46

b) the probability that a randomly chosen dealer wll have an income under $100,000 given that he or she is under 40

=total number of dealers having an income under $100,000 and aged under 40/total number of dealers aged under 40=1500/2500=0.6

c) the probability that a randomly chosen dealer aged 40 and above given that they have an income of $100,000 and over= total number of dealers aged 40 and above and have an income of $100,000 and over/ total number of dealers have an income of 100,000 and over=2500/3500=0.71

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