# Common Core: 7th Grade Math : Represent Sample Spaces for Compound Events: CCSS.Math.Content.7.SP.C.8b

## Example Questions

← Previous 1

### Example Question #29 : Outcomes

Two fair dice are thrown. What is the probability that the difference of the numbers that show on the dice will be exactly ?

Explanation:

The following rolls result in the difference of the dice being :

and the reverse of each of these.

These are  rolls out of a possible , so the probability of this event is

### Example Question #30 : Outcomes

Two fair six-sided dice are thrown. What is the probability that the product of the two numbers rolled is between  and  inclusive?

Explanation:

The rolls that yield a product between  and  inclusive are:

Therefore there are  rolls that fit our criteria out of a total of  possible rolls, so the probability of this outcome is .

### Example Question #1 : Represent Sample Spaces For Compound Events: Ccss.Math.Content.7.Sp.C.8b

Charlie is going to roll a die and flip a coin. What is the probability that he will roll a  and the coin will land with heads facing up?

Explanation:

To help us solve this problem, we can make a tree diagram to show all of the possible outcomes of rolling a die and flipping a coin:

As shown from the diagram, we have  possible outcomes, but there is only one way to roll a  and for the coin to land on heads; thus, the probability is

### Example Question #2 : Represent Sample Spaces For Compound Events: Ccss.Math.Content.7.Sp.C.8b

Charlie is going to roll a die and flip a coin. What is the probability that he will roll a  and the coin will land with tails facing up?

Explanation:

To help us solve this problem, we can make a tree diagram to show all of the possible outcomes of rolling a die and flipping a coin:

As shown from the diagram, we have  possible outcomes, but there is only one way to roll a  and for the coin to land on tails; thus, the probability is

### Example Question #3 : Represent Sample Spaces For Compound Events: Ccss.Math.Content.7.Sp.C.8b

Charlie is going to roll a die and flip a coin. What is the probability that he will roll an even number and the coin will land with heads facing up?

Explanation:

To help us solve this problem, we can make a tree diagram to show all of the possible outcomes of rolling a die and flipping a coin:

As shown from the diagram, we have  possible outcomes. A die has three even numbers: , and . Looking at those numbers on the diagram, we can see that there are three ways to roll an even number and for the coin to land on heads; thus, the probability is

### Example Question #4 : Represent Sample Spaces For Compound Events: Ccss.Math.Content.7.Sp.C.8b

Charlie is going to roll a die and flip a coin. What is the probability that he will roll an odd number and the coin will land with tails facing up?

Explanation:

To help us solve this problem, we can make a tree diagram to show all of the possible outcomes of rolling a die and flipping a coin:

As shown from the diagram, we have  possible outcomes. A die has three odd numbers: , and . Looking at those numbers on the diagram, we can see that there are three ways to roll an odd number and for the coin to land on tails; thus, the probability is

### Example Question #5 : Represent Sample Spaces For Compound Events: Ccss.Math.Content.7.Sp.C.8b

Charlie is going to roll a die and flip a coin. What is the probability that he will roll a  and the coin will land with heads or tails facing up?

Explanation:

To help us solve this problem, we can make a tree diagram to show all of the possible outcomes of rolling a die and flipping a coin:

As shown from the diagram, we have  possible outcomes, but there is only one way to roll a  and the coin can either land on heads or tails; thus, the probability is

### Example Question #6 : Represent Sample Spaces For Compound Events: Ccss.Math.Content.7.Sp.C.8b

Kara is going to roll a die and spin a spinner, shown below. What is the probability that she will roll a  and the spinner will land on yellow?

Explanation:

To help us solve this problem, we can make a tree diagram to show all of the possible outcomes of rolling a die and spinning the spinner:

As shown from the diagram, we have  possible outcomes. There is only one way to roll a six and for the spinner to land on yellow; thus, the probability is

### Example Question #7 : Represent Sample Spaces For Compound Events: Ccss.Math.Content.7.Sp.C.8b

Kara is going to roll a die and spin a spinner, shown below. What is the probability that she will roll an even number and the spinner will land on pink?

Explanation:

To help us solve this problem, we can make a tree diagram to show all of the possible outcomes of rolling a die and spinning the spinner:

As shown from the diagram, we have  possible outcomes. There are three even numbers on a die: ,  and  and for each other those numbers there is one way to spin a pink; thus, the probability is

### Example Question #8 : Represent Sample Spaces For Compound Events: Ccss.Math.Content.7.Sp.C.8b

Kara is going to roll a die and spin a spinner, shown below. What is the probability that she will roll an odd number and the spinner will land on orange?

Explanation:

To help us solve this problem, we can make a tree diagram to show all of the possible outcomes of rolling a die and spinning the spinner:

As shown from the diagram, we have  possible outcomes. There are three odd numbers on a die: ,  and  and for each of those numbers there is one way to spin an orange; thus, the probability is

← Previous 1