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 = [tex]\frac{570}{2100}[/tex]
Probability of None = [tex]\frac{60}{2100}[/tex]
As it is asking for "OR", use the "or rule", i.e., add the probabilities:
P(Prom or None) = [tex]\frac{570}{2100}+\frac{60}{2100}[/tex]
P(Prom or None) = [tex]\frac{630}{2100}[/tex]
P(Prom of None) = 0.3
The probability of a student had went to Prom or none of them is 0.3 or 30%.
