Question

2100 students were surveyed about whether they went to the Homecoming Dance and the Prom. 1470 students went to the Homecoming Dance. 570 students went to Prom only. 360 students went to both the Homecoming Dance and Prom. P (Went to Prom or None).

Answer 1

Answer and Step-by-step explanation: The problem can be solved by using a Venn Diagram.

A Venn Diagram shows the relation between a collection of different sets.

The figure below shows:

1) Students who went only to the Homecoming = 1110

2) Students who went only to the Prom = 570

3) Students who went to both = 360

4) Students who went to none = 60

The question asks for the probability of students who went to Prom or None.

Probability of Prom =
`(570)/(2100)`

Probability of None =
`(60)/(2100)`

As it is asking for "OR", use the "or rule", i.e., add the probabilities:

P(Prom or None) =
`(570)/(2100)+(60)/(2100)`

P(Prom or None) =
`(630)/(2100)`

P(Prom of None) = 0.3

The probability of a student had went to Prom or none of them is 0.3 or 30%.