Page 90 - NUMINO Challenge_D2

Basic Concepts Counting Principle (Two Events Occur at the Same Time)

When two events A and B occur at the same time, let a be the number of
possible outcomes in event A and let b be the number of possible outcomes in
event B. To find the total number of possible outcomes, multiply the number of
possible outcomes for events A and B.

Total number of possible outcomes when events A and B occur at the
same time) a b

There are two possible outcomes, front and back, when you flip a coin. There
are six possible outcomes, 1, 2, 3, 4, 5, and 6, when you roll a die. Therefore,
the total number of possible outcomes, using the Counting Principle, is
2 6 12(outcomes) when you flip a coin and roll a die at the same time.

Example There are three ways to go from village A to village B, and there

are two ways to go from village B to village C. How many possible

ways are there to go from village A to village C by passing through

village B?

a

AB C

b

Class Notes

There are ways, ( , a) and ( , b), to go to village C from village A

by taking road .

There are ways, ( , a) and ( , b), to go to village C from village A

by taking road .

There are ways, ( , a) and ( , b), to go to village C from village A

by taking road .

There are three ways to go from village A to village B, and for each way, there are two
ways to go from village B to village C. Therefore, the number of possible ways to go from

village A to village C by passing through village B is (ways) when the
Counting Principle is used.

87Number of Outcomes