Exercise 23 Page 305

We are given an experiment and want to represent the sample space by making a table. Then we want to find the probability P(less than3 and tails). The sample space of an experiment is the set of all possible outcomes. In this case, the sample space is the result of two stages.

• Spinning a Spinner — 1, 2,3,4, or 5
• Flipping a Coin — heads or tails

Keep in mind that there are several ways to make a table. The part that matters most is that the sample space ends up with all of the possible combinations. To make the table, we will list the outcomes of the first exercise in the first row and the outcomes of the second exercise in the left column.

Outcomes	1	2	3	4	5
Heads
Tails

Now we will pair each possible outcome from the first exercise with the possible outcomes from the second exercise.

Outcomes	1	2	3	4	5
Heads	1H	2H	3H	4H	5H
Tails	1T	2T	3T	4T	5T

Finally, we can find P(less than3 and tails). We can see that there are 10 total outcomes in the sample space and only 2 of them are favorable.

Outcomes	1	2	3	4	5
Heads	1H	2H	3H	4H	5H
Tails	1T	2T	3T	4T	5T

We will use the Probability Formula to find the probability that P(less than3 and tails) occurs.

P=Favorable Outcomes/Possible Outcomes

SubstituteValues

Substitute values

P(less than3 and tails)=2/10

ReduceFrac

a/b=.a /2./.b /2.

P(less than3 and tails)=1/5

CalcQuot

Calculate quotient

P(less than3 and tails)=0.2

WritePercent

Convert to percent

P(less than3 and tails)= 20 %

The probability of rolling a number less than 3 and flipping tails is 15, or 20 %.