Question

A gift shop has a “Scratch and Win” game. When you purchase an item, you

have the opportunity to win a rate of discount. One hundred forty five
tickets have 10% discounts, 135 tickets have 20% discounts, 75 tickets
have 30% discounts, and 50 tickets have 40% discounts.
a) What is the theoretical probability that the first customer will win a 30%
discount? Express as a fraction, decimal, and percent.

Answer 1

`(5)/(27)`,0.185(3.s.f),18.5%(3.s.f.)

Explanation:

1. To find the probability of a customer winning a 30% discount we need to first find how many tickets out of all the tickets have a 30% discount so lets add all the tickets to get a total

145+135+75+50 = 405

out of the 405 tickets 75 tickets have 30% discounts

therefore the probability that the first customer will win a 30% discount is
`(75)/(405)` which simplifies to
`(5)/(27)`

2. Now to convert into a decimal we need to do 5 divided by 27 which comes out to be

0.185185185... (recurring) however we can round it to 3 significant figures (3.s.f)

3. To covert it into a percentage we simply multiply the decimal by 100

0.185 x 100 = 18.5% (3.s.f. as we rounded our decimal to that as well)