A survey carried out on 40 students about when they did their homework over the weekend

F=(homework done on friday)
S=(homework done on saturday/Sunday )
n(f)=20,n(s)=29
How many did both days ?

b did both

draw Venn diagram

fri---both- weekend

|20-b | b |29-b|

20-b + b + 29-b = 40

49 - b = 40

b = 9

11 fri , 9 both , 20 weekend

To determine the number of students who did their homework on both Friday and either Saturday or Sunday, we need to find the intersection of the two sets.

From the given information:
n(f) = 20 (the number of students who did homework on Friday)
n(s) = 29 (the number of students who did homework on either Saturday or Sunday)

However, we do not have the information about the number of students who did homework on both days directly. We need to make use of additional information in order to find the answer.

One possible approach is to use a formula called the "Inclusion-Exclusion principle." According to this principle:

n(f ∩ s) = n(f) + n(s) - n(f ∪ s)

where:
n(f ∩ s) represents the number of students who did homework on both Friday and either Saturday or Sunday.
n(f ∪ s) represents the number of students who did homework on either Friday or Saturday or Sunday (the union of both sets).

Unfortunately, we do not have the value for n(f ∪ s).

Without additional information, it is not possible to determine the exact number of students who did their homework on both Friday and either Saturday or Sunday.