THEORETICAL PROBABILITY OF COMPOUND EVENTS WORKSHEET

Problem 1 :

Jacob rolls two fair number cubes. Find the probability that the sum of the numbers he rolls is 8.

Problem 2 :

A deli prepares sandwiches with one type of bread (white or wheat), one type of meat (ham, turkey, or chicken), and one type of cheese (cheddar or Swiss). Each combination is equally likely. Find the probability of choosing a sandwich at random and getting turkey and Swiss on wheat bread.

Problem 3 :

The combination for Khiem’s locker is a 3-digit code that uses the numbers 1, 2, and 3. Any of these numbers may be repeated. Find the probability that Khiem’s randomly-assigned number is 222.

Detailed Answer Key

Problem 1 :

Jacob rolls two fair number cubes. Find the probability that the sum of the numbers he rolls is 8.

Solution :

Step 1 :

List out all the possible outcomes when two cubes are rolled. 

There are 36 possible outcomes in the sample space. 

Step 2 :

Create a table where each cell represents the sum on two number cubes. 

Then, circle the outcomes that give the sum of 8.

Step 3 :

Find the number of outcomes in which the sum is 8. 

Number of outcomes in which the sum is 8  =  5

Step 4 : 

Find the required probability. 

P (for sum 8)  =  5/36

Problem 2 :

A deli prepares sandwiches with one type of bread (white or wheat), one type of meat (ham, turkey, or chicken), and one type of cheese (cheddar or Swiss). Each combination is equally likely. Find the probability of choosing a sandwich at random and getting turkey and Swiss on wheat bread.

Solution :

Step 1 :

Make a tree diagram to find the sample space for the compound event.

Step 2 :

Find the number of possible outcomes in the sample space.

From the above tree diagram, number of possible outcomes in the sample space is 12.

Step 3 :

Find the number of possible outcomes for turkey and Swiss on wheat bread.

From the above tree diagram, number of possible outcomes for turkey and Swiss on wheat bread is 1.  

Step 3 :

Find the probability of choosing turkey and Swiss on wheat bread at random.

Probability  =  1/12

Problem 3 :

The combination for Khiem’s locker is a 3-digit code that uses the numbers 1, 2, and 3. Any of these numbers may be repeated. Find the probability that Khiem’s randomly-assigned number is 222.

Solution :

Step 1 :

List all the codes that start with 1 and have 1 as a second digit.

(1, 1, 1)

(1, 1, 2)

(1, 1, 3)

Step 2 :

List all the codes that start with 1 and have 2 as a second digit.

(1, 2, 1)

(1, 2, 2)

(1, 2, 3)

Step 3 :

List all the codes that start with 1 and have 3 as a second digit.

(1, 3, 1)

(1, 3, 2)

(1, 3, 3)

Step 4 :

We have now listed all the codes that start with 1. Let us repeat Steps 1–3 for codes that start with 2, and then for codes that start with 3. 

Step 5 :

Find the number of outcomes in the sample space by counting all the possible codes.

There are 27 such codes.

Step 6 :

Find the probability that Khiem’s locker code is 222.

Number of outcomes for  Khiem’s locker code 222  =  1

Probability (Code 222)  =  1/27

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