The venn diagram represents a group of children who swam (left circle) and built sandcastles (right circle) at the beach. match the symbol or description on the left with its corresponding value on the right. s stands for the event “swam” and c stands for the event “built sandcastles.” assume the numbers represent the entire universe. 1. p(s) 0.76 2. p(s or c, but not both) 0.84 3. p(c) 0.60 4. p(s ∪ c) 1.00 5. p(c, but not s) 0.40 6. p(s ∩ c) 0.16

The sample space, is the set of all children involved. Thus,

                   n(Samples space)=n(S)=6+15+4=25.

The letters S and C represent the sets "Swam" and "built castles", clearly.

Let
, , , , , 
be the following events, with the following number of sets:

: S.        n()= number of all those who swam =21.

: S or C, but not both.        n()=6+4=10, because there are 6 of those who swam but not built castles, and 4 of those who built castles but not swam.

: C.         n()=15+4=19.

: S ∪ C.         n()=6+15+4=25.

: C, but not S.         n()=4, as there are only 4 who built castles but not swam.

: S ∩ C.         n()=15, as they are 15 who built castles and swam.


The formula for the probability  of an event  is .

Thus, the probabilities are as follows: