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# Averages, Probability, and Combinations for CBEST Exam Study Guide

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Updated on Mar 29, 2011

In this lesson, you'll have a chance to do sample average questions as well as problems on probability and on the number of possible combinations. These questions may be a little more advanced than those you did in school, but they will not be difficult for you if you master the information in this section.

### Averages

You probably remember how you solved average problems way back in elementary school. You added up the numbers, divided by the number of numbers, and the average popped out. Here's this process in algebraic form:

#### Four Success Steps for Average Problems

1. In order to use the formula , draw a horizontal line.
2. Write in all the information you know. Put the number of numbers under the line and the average beside the line. Unless you know the whole sum, leave the top of the line blank.
3. Multiply the number of numbers by the average. This will give you the sum of the numbers.
4. Using this sum, solve the problem.

What makes CBEST average problems more difficult is that not all of the numbers will be given for you to add. You'll have to find some of the numbers.

#### Sample Average Question

1. Sean loved to go out with his friends, but he knew he'd be grounded if he didn't get 80% for the semester in his English class. His test scores were as follows: 67%, 79%, 75%, 82%, and 78%. He had two more tests left to go. One was tomorrow, but his best friend Jason had invited him to his birthday party tonight. If he studied very hard and got 100% on his last test, what could he get by with tomorrow and achieve the 80%?
1. 65%
2. 72%
3. 76.2%
4. 79%
5. 80.2%

Use the four Success Steps to solve the problem.

1. Draw the horizontal line:
2. Write in the information: = 80%
3. Multiply the number of numbers by the average to obtain the sum of the numbers: 7 × 80 = 560
4. The number 560 has to be the final sum of the numbers. So far, if you add up all the scores, Sean has a total of 381.With the 100 he plans to get on the last test, his total will be 481. Since he needs a sum of 560 for the average of the seven tests to be 80, he needs 79 more points. The answer is choice d.

#### Sample Average Question

1. On an overseas trip, Jackie and her husband are allowed five suitcases that average 110 pounds each. They want to pack in all the peanut butter and mango nectar they can carry to their family in Italy. They weighed their first four suitcases and the weights were as follows: 135, 75, 90, and 120 pounds. How much weight are they allowed to carry in their fifth bag?

1. Draw the horizontal line:
2. Write in the information: = 110
3. Multiply the number of numbers by the average to obtain the sum of the numbers: 5 × 110 = 550.
4. The total weight they can carry is 550 lbs. and they already have 420 lbs. (135 + 75 + 90 + 120), so the fifth suitcase can weigh as much as 550 – 420, or 130 lbs.

#### Four Success Steps for Frequency Chart Questions

1. Read the question and look at the chart. Make sure you understand what the different columns represent.
2. If a question asks you to find the average, multiply the numbers in the frequency column by the numbers in the column of data values.
3. Add the figures you got by multiplying.
4. Divide the total sum by the sum of the left column. This will give you the average.