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Dropdown 1: 11 out of 20
Dropdown 2: 40%
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Difficulty:
65%
(hard)
Question Stats:
61% (02:41) correct
39%
(02:42)
wrong
based on 1141
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Use the drop down menus to complete each statement based on the information given in the diagram.
A. If one teacher is selected at random from those surveyed, the probability that he or she holds a second job, rents out one or more rooms in his or her home, or both is .
B. Of the teachers surveyed hold a second job.
Attachment:
SET.PNG [ 61.84 KiB | Viewed 9434 times ]
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Official Answer
Dropdown 1: 11 out of 20
Dropdown 2: 40%
29 Sep 2024, 12:06
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Spoorthii
Sure!
1. We are asked to find the probability that "if one teacher is selected at random from those surveyed, that he or she holds a second job, rents out one or more rooms in his or her home, or both".
2. Probability is much easier to understand as sets and we're picking a random person from the all sets together. There are three sets (holds a second job, rents out one or more rooms, or both) and the total probability is the union of the 3.
3. Let's visualize our initial Venn diagram.
4. The first set is the people who hold a second job.
5. The second set is the people who rent out one or more rooms.
6. The third set is the people who do/have both.
7. The union of all 3 sets is just the third set. The probability to pick someone in that area is \(= \frac{people \ in \ red}{all \ people} = \frac{5 + 3 + 3}{5 + 3 + 3 + 9} = \frac{11}{20}\).
8. So, the answer should be \(\frac{11}{20}\).
I hope that helped you!
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29 Sep 2024, 11:41
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For the first question you answer like this:
probability of NOT renting, but holding a second job (not part of any circle)= 5*20 / 400
probability of renting, but NOT holding a second job (intersection) = 3*20 /400
probability of renting AND holding a second job (only a section of the right circle) = 3*20 /400
Total probability (sum of all of the above) = 11/20
probability of NOT renting, but holding a second job (not part of any circle)= 5*20 / 400
probability of renting, but NOT holding a second job (intersection) = 3*20 /400
probability of renting AND holding a second job (only a section of the right circle) = 3*20 /400
Total probability (sum of all of the above) = 11/20
