ASVAB averages and probability
An average is the total divided by the count, so total equals average times count; that one fact solves most average questions, including missing scores. Probability is favorable outcomes divided by total outcomes. Multiply for "and" with independent events, and subtract from 1 for "at least one".
How do you find the average on the ASVAB?
Add the values and divide by how many there are. Average and mean are the same thing on the test. These items appear mostly as Arithmetic Reasoning word problems, and you work them by hand because "you cannot use a calculator" (What to Expect).
| Measure | How to find it | Example: 3, 5, 5, 8, 9 |
|---|---|---|
| Mean | sum ÷ count | 30 ÷ 5 = 6 |
| Median | middle value after sorting | 5 |
| Mode | most frequent value | 5 |
| Range | largest − smallest | 9 − 3 = 6 |
| Weighted average | sum of (value × count) ÷ total count | see below |
Example: Find the mean and median of 78, 85, 92, 88 and 77.
- Sum: 78 + 85 = 163, 163 + 92 = 255, 255 + 88 = 343, 343 + 77 = 420.
- Mean: 420 ÷ 5 = 84.
- Sort: 77, 78, 85, 88, 92. The middle value is 85.
Answer: mean 84, median 85
Speed trick for the mean: pick a base near the middle, such as 80, and average the differences. 78, 85, 92, 88, 77 are −2, +5, +12, +8, −3 from 80. Those add to 20, and 20 ÷ 5 = 4, so the mean is 84.
How do you find a missing value when you know the average?
Multiply the target average by the count to get the total you need, then subtract what you already have.
Example: You want an 85 average on four tests. Your first three scores are 82, 88 and 79. What do you need on the fourth?
- Needed total: 85 × 4 = 340.
- Current total: 82 + 88 + 79 = 249.
- Fourth score: 340 − 249 = 91.
- Check: (82 + 88 + 79 + 91) ÷ 4 = 340 ÷ 4 = 85.
Answer: 91
How do weighted averages work?
When groups have different sizes, multiply each group's average by its size, add, and divide by the total size. Averaging the two averages is only correct when the groups are the same size.
Example: A class of 12 averaged 80 on a test and a class of 18 averaged 90. What is the average for all 30 students?
- Points in the first class: 12 × 80 = 960.
- Points in the second class: 18 × 90 = 1,620.
- Total: 960 + 1,620 = 2,580 over 30 students.
- 2,580 ÷ 30 = 86.
Answer: 86 (not 85)
The answer is closer to 90 because the larger class scored 90. If 85 appears in the choices, it is the trap for averaging the averages.
How do you find a basic probability?
Count the favorable outcomes and divide by the total number of equally likely outcomes. Simplify the fraction.
Example: A bag holds 5 red, 3 blue and 2 green marbles. What is the probability of drawing a blue marble?
- Favorable: 3 blue marbles.
- Total: 5 + 3 + 2 = 10.
- Probability: 3/10.
Answer: 3/10 (0.3 or 30%)
The probability that something does not happen is 1 minus the probability that it does. The chance of not drawing blue is 1 − 3/10 = 7/10.
Example: Two dice are rolled. What is the probability that the sum is 7?
- Total outcomes: 6 × 6 = 36.
- Pairs that sum to 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). That is 6.
- 6/36 = 1/6.
Answer: 1/6
How do you find the probability of two events?
For "A and B" with independent events, multiply the probabilities. If you draw without putting the first item back, the second probability changes because there is one fewer item.
Example: From the same bag (5 red, 3 blue, 2 green), you draw two marbles without replacement. What is the probability both are red?
- First draw: 5 red out of 10, so 5/10.
- Second draw: 4 red left out of 9, so 4/9.
- Multiply: 5/10 × 4/9 = 20/90 = 2/9.
Answer: 2/9
Example: A coin is flipped three times. What is the probability of getting at least one head?
- The only way to get no heads is tails, tails, tails: 1/2 × 1/2 × 1/2 = 1/8.
- At least one head is everything else: 1 − 1/8 = 7/8.
Answer: 7/8
"At least one" is almost always faster as 1 minus the probability of none.
How does adding or removing a value change the average?
Work with totals, not averages. Turn the old average into a total, add or remove the value, then divide by the new count.
Example: Five numbers average 12. A sixth number, 18, is added. What is the new average?
- Old total: 12 × 5 = 60.
- New total: 60 + 18 = 78. New count: 6.
- New average: 78 ÷ 6 = 13.
Answer: 13
A quick reasonableness check: the new value is above the old average, so the average must rise, but only a little because it is shared across six numbers. A value equal to the old average leaves it unchanged.
For consecutive numbers or any evenly spaced list, the average equals the middle value, or the average of the first and last values. The average of 11, 12, 13, 14 and 15 is 13 without adding anything. This also works for evenly spaced lists with an even count: the average of 2, 4, 6, 8 is (2 + 8) ÷ 2 = 5.
How do you count outcomes and handle "or" probability?
When you make several independent choices, multiply the number of options for each choice. This counting rule gives you the total outcomes for many probability questions.
Example: You have 3 shirts, 4 pairs of pants and 2 pairs of shoes. How many different outfits can you make?
- Each shirt can go with each pair of pants: 3 × 4 = 12.
- Each of those can go with either pair of shoes: 12 × 2 = 24.
Answer: 24 outfits
For "A or B", count every outcome that fits either condition, but count overlaps only once. If the two events cannot happen together, you can simply add their probabilities.
Example: A card is drawn from cards numbered 1 to 20. What is the probability that the number is a multiple of 3 or a multiple of 5?
- Multiples of 3: 3, 6, 9, 12, 15, 18. That is 6.
- Multiples of 5: 5, 10, 15, 20. That is 4.
- 15 is in both lists, so count it once: 6 + 4 − 1 = 9.
- Probability: 9/20.
Answer: 9/20
Listing outcomes is a reliable fallback when you are not sure which rule applies. With small numbers like these, a list takes less than a minute and removes the guesswork.
What mistakes do people make on average and probability questions?
- Averaging averages when the groups have different sizes.
- Forgetting to sort the list before finding the median.
- Using the same total for the second draw when items are not replaced.
- Adding probabilities for "and" questions. "And" multiplies; "or" (for events that cannot both happen) adds.
- Leaving a probability above 1. If you get more than 1, something went wrong.
Averages often mix with other topics, such as rates or money. See the word problem types and the formula sheet, then try timed items on the Arithmetic Reasoning practice page.
Practice questions
Work each one on paper first, then open the explanation. These are original AptiStep items, not real ASVAB questions.
What is the mean of 14, 18, 21, 23 and 29?
- 20
- 22
- 21
- 23
Show answer and explanation
Answer: C. 21
Add the numbers: 14 + 18 = 32, 32 + 21 = 53, 53 + 23 = 76, 76 + 29 = 105. Divide by the count of 5: 105 ÷ 5 = 21.
What is the median of 9, 3, 7, 12, 5 and 10?
- 7
- 8
- About 7.7
- 12
Show answer and explanation
Answer: B. 8
Sort first: 3, 5, 7, 9, 10, 12. With six values, the median is the average of the two middle ones, 7 and 9: (7 + 9) ÷ 2 = 8. About 7.7 is the mean (46 ÷ 6), not the median.
The average of five numbers is 30. Four of them are 26, 34, 28 and 31. What is the fifth?
- 30
- 29
- 32
- 31
Show answer and explanation
Answer: D. 31
Total needed: 30 × 5 = 150. The four known numbers add to 26 + 34 + 28 + 31 = 119. Fifth number: 150 − 119 = 31.
You work 8 hours at $15 per hour and 12 hours at $20 per hour. What is your average hourly pay?
- $18.00
- $17.50
- $17.00
- $18.50
Show answer and explanation
Answer: A. $18.00
Total pay: 8 × 15 = 120 and 12 × 20 = 240, so 360. Total hours: 20. Average: 360 ÷ 20 = $18. The $17.50 choice averages the two rates, ignoring that you worked more hours at $20.
A drawer has 4 black, 6 white and 2 blue socks. If you pick one at random, what is the probability it is not white?
- 1/3
- 1/2
- 1/6
- 2/3
Show answer and explanation
Answer: B. 1/2
There are 4 + 6 + 2 = 12 socks. Not white means black or blue: 4 + 2 = 6. Probability 6/12 = 1/2. Or use the complement: P(white) = 6/12 = 1/2, so P(not white) = 1 − 1/2 = 1/2.
You flip a coin and roll a six-sided die. What is the probability of heads and an even number?
- 1/2
- 1/6
- 1/4
- 3/4
Show answer and explanation
Answer: C. 1/4
The events are independent, so multiply. P(heads) = 1/2. P(even) = 3/6 = 1/2. Together: 1/2 × 1/2 = 1/4. Adding them (1/2 + 1/2 = 1) is the "and" mistake.
A box has 3 red and 2 white marbles. You draw two without replacement. What is the probability both are white?
- 4/25
- 1/5
- 2/5
- 1/10
Show answer and explanation
Answer: D. 1/10
First draw: 2 white out of 5, so 2/5. One white is gone, so the second draw is 1 white out of 4, or 1/4. Multiply: 2/5 × 1/4 = 2/20 = 1/10. The 4/25 choice assumes the first marble was put back.
You roll a six-sided die twice. What is the probability of rolling at least one 6?
- 11/36
- 1/3
- 1/36
- 25/36
Show answer and explanation
Answer: A. 11/36
Use the complement. P(no 6 on one roll) = 5/6. P(no 6 on both) = 5/6 × 5/6 = 25/36. P(at least one 6) = 1 − 25/36 = 11/36. Adding 1/6 + 1/6 = 1/3 double counts the case where both rolls show 6.
Frequently asked questions
Is probability really on the ASVAB?
Mathematics Knowledge covers "high school mathematics principles" (official ASVAB), and basic probability is part of that. Expect simple counting and fraction probability, not advanced statistics.
What is the difference between mean and median?
The mean uses every value (sum divided by count). The median is the middle value after sorting. One very large or very small number moves the mean a lot but barely moves the median.
Should I write probability as a fraction, decimal or percent?
Match the answer choices. A fraction is usually easiest to compute by hand, and you can convert at the end: 3/10 = 0.3 = 30%.
Sources
Checked November 14, 2026. AptiStep is an independent study site; confirm anything that affects your enlistment with a recruiter.