In a survey of 50 students, 60% said that they have a cat. Of the students who have a cat, 70% also have a dog. Of the students who do not have a cat, 75% have a dog. Complete the two-way table.

| Dog | No Dog | Total
----------------|----------|---------------|----------------
Cat | | |
No Cat | | |
Total | | |

Here the total number of students is 50. 60% have a cat .Therefore 60% of 50 is 30 and thus 30 students have a cat. remaining 40% doesn't have a cat that is 20 students are there with out a cat .In the 30 students who have cat 70% that is 21 students have dog. And in those 20 persons 75% have dog.Therefore 15 persons have dog in those 20 students who does not have cat.

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jbiain jbiain · Answer 2 · 2019-10-16T13:56:44+02:00

Answer:

| Dog | No Dog | Total

| 36 | 14 | 50

| Cat | No Cat | Total

| 30 | 20 | 50

Step-by-step explanation:

In a survey of 50 students, 60% said that they have a cat. In mathematical terms:

Cat = 0.6*50 = 30

If 60% have a cat, then 40% don't have a cat

No Cat = (1-0.6)*50 = 20

Because there are 2 options, the addition of them has to give the total amount of students

Total = Cat + No Cat = 50

Of the students who have a cat, 70% also have a dog. Of the students who do not have a cat, 75% have a dog. In mathematical terms:

Dog = Cat*0.7 + No Cat*0.75 = 30*0.7 + 20*0.75 = 36

Following the same logic as before, if 70% of students who have a cat also have a dog, then 30% of them don't have a dog. Same analysis for the students who do not have a cat.

No Dog = Cat*(1-0.7) + No Cat*(1-0.75) = 30*(1-0.7) + 20*(1-0.75) = 14

Again, the addition of the 2 options has to give the total amount of students

Total = 50