The 12 fish in Ava's aquarium are orange, striped, or both orange and striped. If 2/3 of the fish are orange, and 1/2 are striped, how many are both orange and striped?

Question

Due in a few hours! Thank you!

Answer 1

2/3 + 1/2 = 4/6 + 3/6 = 7/6 = 1 + 1/6

1/6 of 12 = 12/6 = 2 fish are both

Answer 2

9 striped + 6 orange = 15...but this counts twice fish that are both orange and striped

Since there are only 12 fish, 3 must have been counted twice, i.e. there are 6 only orange, 3 only striped and 3 both orange and striped.

This is an example of the principle of inclusion-exclusion...and it the basis for the statement in probability that P(A or B)=P(A)+P(B)-P(A and B)

If unclear, draw a Venn diagram.