Suppose that in a population of shoppers, the proportion of people who had visited supermarket A last month is 0.22. Also that in the same population, the proportion of people who had visited supermarket B last month is 0.46. The proportion of shoppers who had visited both supermarket A and supermarket B last month is 0.10.
What proportion of people in this population had visited supermarket A or supermarket B or both last month? (Give your answer to two decimal places.)
.22 + .46 - .10 = .58
To find the proportion of people who had visited supermarket A or supermarket B or both last month, we need to calculate the union of the two proportions:
Proportion of people who visited supermarket A = 0.22
Proportion of people who visited supermarket B = 0.46
Proportion of people who visited both supermarket A and supermarket B = 0.10
To find the proportion of people who visited either supermarket A or supermarket B, we can add the proportions of each supermarket and subtract the proportion of people who visited both:
Proportion of people who visited either supermarket A or supermarket B = (Proportion of people who visited supermarket A) + (Proportion of people who visited supermarket B) - (Proportion of people who visited both)
= 0.22 + 0.46 - 0.10
= 0.58
So, the proportion of people who had visited supermarket A or supermarket B or both last month is 0.58.
To find the proportion of people in the population who had visited supermarket A or supermarket B or both last month, we can use the principle of inclusion-exclusion.
First, let's find the proportion of people who visited supermarket A or supermarket B. To do this, we add the proportions of people who visited supermarket A and supermarket B separately and subtract the proportion of people who visited both:
Proportion(A or B) = Proportion(A) + Proportion(B) - Proportion(A and B)
= 0.22 + 0.46 - 0.10
= 0.58
Therefore, the proportion of people who visited supermarket A or supermarket B is 0.58.
Please note that in this question, we do not consider the "and" condition for supermarket A and supermarket B, as we are only interested in the proportion of people who visited either one or both supermarkets.