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According to a survey, 49% of U.S. adults have purchased a state lottery ticket in the past 12 months. Of these 49%, about 27.5% have annual incomes less than $36,000. (Adapted from Gallup) (a) Find the probability that a randomly selected U.S. adult purchased a state lottery ticket in the past 12 months and has an annual income less than $36,000. (b) Find the probability that a randomly selected U.S. adult who purchased a state lottery ticket in the past 12 months has an annual income greater than or equal to $36,000. (c) Would it be unusual for a randomly selected U.S. adult to have purchased a state lottery ticket in the past 12 months and to have an annual income less than $36,000? Explain.

Answer :

Answer:

a. P = 0.13475

b. P = 0.725

c. No. About 13% of the U.S. adults have purchased a lottery ticket in the last 12 months and have an income below $36,000.

Step-by-step explanation:

Probability of selecting a person that has  purchased a lottery ticket: P("L")=0.49

Probability of having an income less than $36,000, given that has purchased a lottery ticket in the last 12 months P("I<36" | "L")=0.275.

a. Probability that a randomly selected U.S. adult purchased a state lottery ticket in the past 12 months and has an annual income less than $36,000

P("L"&"I<36") = P("I<36" | "L") * P("L") = 0.275 * 0.49 = 0.13475

b. Probability that a randomly selected U.S. adult who purchased a state lottery ticket in the past 12 months has an annual income greater than or equal to $36,000.

P("I>36" | "L") = 1 - P("I<36" | "L") = 1 - 0.275 = 0.725

c. Would it be unusual for a randomly selected U.S. adult to have purchased a state lottery ticket in the past 12 months and to have an annual income less than $36,000

No. About 13% of the U.S. adults have purchased a lottery ticket in the last 12 months and have an income below $36,000.

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