Exercise 4 Page 302

We are given an experiment and want to represent the sample space by making an a table. Then we want to find the probability P(at most4 and heads). 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.

• Rolling a Number Cube — 1, 2,3,4,5, or 6
• 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	6
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	6
Heads	1H	2H	3H	4H	5H	6H
Tails	1T	2T	3T	4T	5T	6T

Finally, we can find P(at most4 and heads). We can see that there are 12 total outcomes in the sample space and only 4 of them are favorable.

Outcomes	1	2	3	4	5	6
Heads	1H	2H	3H	4H	5H	6H
Tails	1T	2T	3T	4T	5T	6T

We will use the Probability Formula to find the probability that P(at most4 and heads) occurs.

P=Favorable Outcomes/Possible Outcomes

SubstituteValues

Substitute values

P(at most4 and heads)=4/12

ReduceFrac

a/b=.a /4./.b /4.

P(at most4 and heads)=1/3

CalcQuot

Calculate quotient

P(at most4 and heads)=0.333333...

WritePercent

Convert to percent

P(at most4 and heads)= 33.333333... %

WriteSum

Write as a sum

P(at most4 and heads)= (33+ 0.333333... ) %

WriteAsFrac

Write as a fraction

P(at most4 and heads)= (33+ 1/3) %

AddTerms

Add terms

P(at most4 and heads)= 33 13 %

The probability of rolling at most 4 and flipping heads is 13, or 33 13 %.