Question

The survey results of the towns favorite holiday were displayed in a newspaper as described37% of people enjoy Fourth of July•28% of people enjoy New Years Eve42% of people enjoy Memorial DayC5% of people enjoy all three12 % of people enjoy New Years Eve and Memorial Day•18 % of people enjoy Fourth of July and New Years Eve13% of people enjoy Memorial Day onlyWhat percentage of people enjoy New Years Eve only?

Answer 1

In order to calculate the percentage that enjoy New Years Eve only, we can use the diagram and formula below:

Using F to represent Fourth of July, N to represent New Years Eve and M to represent Memorial Day, the formula is:

`P(N\text{ only})=P(N)-P(F\text{ and }N)-P(M\text{ and }N)+P(all\text{ }three)`

From the given data, we have:

P(N) = 28% = 0.28

P(F and N) = 18% = 0.18

P(M and N) = 12% = 0.12

P(all three) = 5% = 0.05

So P(N only) is:

`\begin{gathered} P(N\text{ only})=0.28-0.18-0.12+0.05\\ \\ P(N\text{ only})=0.03=3\% \end{gathered}`