Question

the table below relates the amount of time consumers spend shopping on the internet per month with their annual income. what is the probability that a randomly selected consumer either spends 0 - 2 hours per month shopping on the internet or has an annual income below $40,000? the probability that a consumer either has an annual income below $40,000 or spends 0 - 2 hours per month shopping on the internet is (type a decimal rounded to two decimal places.)

Explanation:

Step1: Recall the formula for the probability of the union of two events

The formula for \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). Let \(A\) be the event that a consumer spends \(0 - 2\) hours per month shopping on the Internet and \(B\) be the event that a consumer has an annual income below \(\$40,000\).

Step2: Calculate \(P(A)\), \(P(B)\) and \(P(A\cap B)\)

• \(P(A)=\frac{n(A)}{n(S)}\), where \(n(A) = 539\) (the total number of consumers who spend \(0 - 2\) hours) and \(n(S)=1568\) (the total number of consumers). So \(P(A)=\frac{539}{1568}\).
• \(P(B)=\frac{n(B)}{n(S)}\), where \(n(B) = 564\) (the total number of consumers with income below \(\$40,000\)). So \(P(B)=\frac{564}{1568}\).
• \(P(A\cap B)=\frac{n(A\cap B)}{n(S)}\), where \(n(A\cap B) = 252\) (the number of consumers who spend \(0 - 2\) hours and have income below \(\$40,000\)). So \(P(A\cap B)=\frac{252}{1568}\).

Step3: Substitute the values into the formula

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Answer:

\(0.52\)