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 ?

1 Answer
Michelle
Jun 27, 2017

#2/3#

Explanation:

We want to find the probability of landing on an even number or a multiple of 3, so we should use the addition rule for the union of two events:

#P(A or B) = P(A) + P(B) - P(A and B)#

Let's make

  • A = the probability of landing on an even number, and
  • B = the probability of landing on a multiple of 3

What is P(A) (the probability of landing on an even number? 2, 4, 6, 8, 10, 12, 14, 16, and 18 are all even, so P(A) is #9/18#.

What is P(B) (the probability of landing on a multiple of 3? 3, 6, 9, 12, 15, and 18 are multiples of 3, so P(B) is #6/18#.

What is P(A and B) (the probability of landing on an even number that's also a multiple of 3)? 6, 12, and 18 are all even AND multiples of 3. So P(A and B) is #3/18#.

Now we can plug our values into the equation!

#P(A or B) = P(A) + P(B) - P(A and B)#

#P(A or B) = 9/18 + 6/18 - 3/18#

#P(A or B) = 12/18#

#P(A or B) = 2/3#

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