Question

Emily is playing a board game that has a spinner divided into equal sections numbered 1 to 18.
The probability of the spinner landing on an even number or a multiple of 3 is . The probability of the spinner landing on an odd number or a number between 4 and 15 (both numbers excluded) is .

Answer 1

let's handle each part of the question separately:

part 1: The probability of the spinner landing on an even number or a multiple of 3 is .

- "even number or a multiple of 3"
to find a list of outcomes that are even or a multiple of 3:
- count how many outcomes between 1 and 18 are even
- count how many outcomes between 1 and 18 are multiples of 3
- count how many outcomes between 1 and 18 are even AND multiples of 3

add the first two counts together, then subtract the third count, so that numbers that are even AND multiples of 3 don't get double counted

then divide by 18, since there are 18 total outcomes

Answer 2

part 2: "The probability of the spinner landing on an odd number or a number between 4 and 15 (both numbers excluded) is ."
- count the number of odd numbers between 1 and 18
- count the number of numbers between 4 and 15 (so all the numbers from 5 up to 14)
- count the number of numbers that are common to both sets (a.k.a the odd numbers between 5 and 14)

as before, subtract the third count from the first two counts, then divide by 18