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# Which rule do I apply?

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About 13​% of the population of a large country is hopelessly romantic. If two people are randomly​ selected, what is the probability both are hopelessly romantic​? What is the probability at least one is hopelessly romantic​?

Oct 9, 2019

#1
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13%,

So lets pretend that 13 people are hOpLeSsLY rOMaNTiC, and that there is 100 people.

To find the probability for the first question, we find the combination of 2 chosen out of 13 over the combinatino fo 2 chosen out of 100

So

78

4950

13/825

Oct 9, 2019
#2
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Then you can find the probability where one is hOpLeSsLY rOMaNTiC out of the two chosen. Then you can add that to the answer of the first question.

I will let you find that out

CalculatorUser  Oct 9, 2019
#3
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You use combination to find cases

And the ruel for probability is the number of selected cases OVER all possible cases.

CalculatorUser  Oct 9, 2019
#4
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For the first question, the probability of the first person selected being hopelessly romantic is 13/100, and the probability for the second person being hopelessly romantic is 13/100

Multiply these to find the probability of them both being hr: 13/100*13/100 to get 1.69% chance of them both being randomly selected.

(apply the multiplication of probabilities rule)

For the second one you should be able to add the probabilities of each person being hr (13/100+13/100), but the numbers wern't working for me. Maybe find find 1-(neither hr)-(both hr) to get the probability of only one of them.

CU, your approach to treat it like there are 100 people and 13 are hr dousn't work because there arn't only 100 people; there is a whole pupulation and your method undercounts because it has to deal with not being able to choose a person twice.

Oct 9, 2019