Question

of 120 visitors to an amusement park, 84 stayed for at least 3 hours, 76 spent at least $20, and 60 stayed for at least 3 hours and spent at least $20. What is the probability that a randomly selected visitor stayed for at least 3 hours and spent less than $20?
A. 2/15
B. 1/5
C. 19/24
D. 1/2

Answer 1

Fill in the numbers in the three sections formed by the venn diagram.

Answer 2

The center portion shared by both circles represents the number of people who stayed at least 3 hours AND spent more than $20. This number is given and so you can fill this number first.

Answer 3

so i filled the venn diagram in.. but i dont know... like do i take 84÷60? and then simplify it?

Answer 4

What numbers did you put in the three areas?

Answer 5

so i followed your venn diagram and i put 84 60 and 76... did i do that correctly?

Answer 6

The center portion is 60. That is correct. But in the left area you need to subtract 60 from 84 and put that number. That way you add up the two numbers in the entire left circle you will get 84. Same logic on the right circle.

Answer 7

good i got that too

Answer 8

What does the number 24 represent?

It is in the circle that represents people who stayed at least 3 hrs.
But it is not in the shared area which represents people who stayed 3 hrs. AND
spent at least $20. Therefore, the 24 must represent the number of people who stayed at least 3 hrs. AND spent LESS THAN $20.

So 24 is the number we are interested. There are 120 visitors and 24 is the number of people who stayed at least 3 hrs. AND spent LESS THAN $20.
The probability: desired outcome / total possibilities = 24 / 120 = ?

Answer 9

ohh okay...now i understand. I got 24/120=1/5 (B)

Answer 10

yes.

Answer 11

thank you sir for taking your time to show me how to solve this problem :D

Answer 12

You are welcome.