Results of a survey of fifty students indicate that 30 like red jellybeans, 29 like green jellybeans, and 17 like both red and green jellybeans. How many of the students surveyed like neither red nor green jellybeans?

8 Students

Step-by-step explanation:

Total Number of Students= 50

Number of students who like red jellybean ,n(R)=30

Number of students who like green jellybean, n(G) =29

Number of students who like red and green jellybean, n(R∩G) =17

We denote by n(R∪G)ᶜ the number who like neither red nor green jellybeans.

Now, using set theory,

n(R∪G)=n(R)+n(G)-n(R∩G)+n(R∪G)ᶜ

50=30+29-17+n(R∪G)ᶜ

50=42+n(R∪G)ᶜ

n(R∪G)ᶜ= 50-42

=8

Therefore, the number of students who like neither red nor green jellybeans= 8

Note: This problem can also be solved using the Venn Diagram Approach

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: