Question

According to a recent study, 60% of households from a certain large region no longer have a landline and instead only have cell phone service. Suppose three households from the region are selected at random. What is the probability that all three have cell phone service only?

Answer 1

The probability that all three randomly selected households have only cell phone service is 21.6%, calculated by multiplying the probability for one household (60%) by itself two more times for the additional households.

Step-by-step explanation:

The student is interested in calculating the probability that all three randomly selected households from a region will have cell phone service only. Given that 60% (or 0.60 as a decimal) of households in the region have only cell phone service, we need to calculate the probability that three households, chosen independently, all fall into this category. This is a straightforward multiplication problem because the selections are independent.

The probability that the first household has only cell phone service is 0.60. The same goes for the second and third households. To find the joint probability, we multiply these probabilities:

P(All three households have cell phone service only) = P(Household 1) * P(Household 2) * P(Household 3)

= 0.60 * 0.60 * 0.60

= 0.216

Therefore, there is a 21.6% chance that all three randomly selected households will have only cell phone service.