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39.8% of consumers believe that cash will be obsolete in the next 20 years. Assume that 7 customers are randomly selected. Find the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years. What is the probability?

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adioabiola

Here, we are required to find the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years.

The correct answer is Pr(C & fewer than 3) = 0.171

Let Pr(C) be the number of consumers who believe that cash will be obsolete in the next 20 years.

Therefore, since 39.8% believe so,

  • Pr(C) = 39.8/100 = 0.398

If 7 consumers are selected randomly, the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years will be;

  • Probability of 2 out 7 to believe so or Probability of 1 out of 7 to believe so.

  • Pr(2/7) + Pr (1/7).

Therefore the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years is;

  • Pr (fewer than 3) = (2/7) + (1/7)
  • Pr (fewer than 3) = 3/7

Therefore, the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years is ;

  • Pr(C) × Pr (fewer than 3)
  • i.e 0.398 × (3/7) = 0.171

Therefore, the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years is ;

Pr(C & fewer than 3) = 0.171

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