# Calculus Check

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A survey of one thousand people found that 70% of the people have a
CD player, 85% have a telephone, and 45.2% have a computer. At
least how many people have all three objects?

Is the answer 258, because that's what I keep getting?

• Calculus Check -

452 have a computer. That number could include at most 150 with no telephone, but probably fewer. So at least 302 have both computer and phone. The 300 with no CD player could be among that 302, but there are probably fewer. So at least 2 have all three. The most likely number having all three, if the distributions are uncorrelated, is 1000 x 0.452 x 0.7 x 0.85 = 269, but that is not what they ask for.

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