Probability

Question

In a class of 80 students, 40 are girls and 40 are boys. Also, exactly 50 students wear glasses. Then the set of all possible numbers of boys without glasses is ?

I dont understand as how to make an assumption as how many boys & girls wear the glasses😐

Thanks alot.

Answer 1

80 students

40 boys and 40 girls

50 students wear glasses

possible number of boys without glasses

 

here are the possibilities:

40 girls wear glasses so 10 boys wear glasses-30 boys don't wear glasses

39 girls wear glasses so 11 boys wear glasses-29 boys don't wear glasses

38 girls wear glasses, 12 boys do, 28 don't

37 girls wear glasses, 13 boys do, 27 don't

.

.

30 girls wear glasses, 20 boys do, 20 don't

29 girls wear glasses, 21 boys do, 19 don't

.

.

21 girls wear glasses, 29 boys do, 11 don't

20 girls wear glasses, 30 boys do, 10 don't

.

.

15 girls wear glasses, 35 boys do, 5 don't

14 girls do, 36 boys do, 4 don't

13 girls do, 37 boys do, 3 don't

12 girls do, 38 boys do, 2 don't

11 girls do, 39 boys do, 1 doesn't

10 girls do, 40 boys do, 0 boys don't

the range is from 0 to 30 boys who don't wear glasses

0,1,2,3,4,...,26,27,28,29,30 are the possible number of boys who don't wear glasses

 

A. is the answer

Answer 2

Lakisha, I suspect the problem wants you to find out the possible range of numbers of boys without glasses.

 

heres a way to attack it: 

First, try to assign glasses to boys and girls so that the LARGEST number of boys have no glasses. Call this number “max”.

Second, try to assign glasses to boys and girls so that the SMALLEST number of boys have no glasses. Call this number “min”.

Finally, the answer to the problem is “all the integers from min to max inclusive”