Digital SAT · Probability & Two-Way Tables

How to Solve Basic Probability on the Digital SAT

Probability is favorable outcomes over total outcomes. Count how many results fit the event, count all the possible results, and write the fraction. When the setup shifts, like removing an item or drawing without replacement, count both again before writing the new probability. Keep the sample consistent and the fraction takes care of itself.

Written from Perfect1600’s analysis of every basic probability question in our bank·Method checked against the current Bluebook test

per test: less than 1 per test
typical difficulty: Mostly easy
practice questions: 40

How we counted

Frequency reflects how often this question type appears on a full-length Digital SAT. The difficulty mix reflects every question of this type across our bank.

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What the question bank shows

count both

Favorable over total

The event over all outcomes; both can shift when the group changes.

count only

No calculator

A counting task, not a graphing one.

recount

After a change

Removing or drawing items moves both the top and bottom of the fraction.

How to recognize basic probability questions

An item is chosen at random from a described group.
The question asks for the probability of a particular outcome.
The group changes, such as removing some items or a second draw.
Choices are fractions, decimals, or percents.

Why students miss these

The formula is simple, so the errors are all in the counting. People leave the total unchanged after an item is removed, count outcomes that do not fit as favorable, or divide by a part instead of the true total. When items are removed or drawn, both the top and the bottom of the fraction can move, and updating only one gives the wrong answer.

The step-by-step method

1
Count the favorable outcomes
Count the results that fit the event described.
2
Count the total outcomes
Count every possible result in the current group.
3
Write the fraction
Favorable over total; simplify or convert to a decimal or percent if asked.
4
Update after a change
If items are removed or drawn, recount both the favorable and the total before writing the new probability.

Worked examples

Easy example

A set of 16 tiles consists of 3 labeled A, 5 labeled B, and 8 labeled C. If one tile is selected at random, what is the probability of selecting a tile labeled B?

\frac{3}{16}

\frac{5}{16}

\frac{8}{16}

\frac{13}{16}

A: Incorrect. This is the probability of selecting a tile labeled A.

B: Correct. There are 5 tiles labeled B out of 16 total, so the probability is $\frac{5}{16}$ .

C: Incorrect. This is the probability of selecting a tile labeled C.

D: Incorrect. This counts the tiles not labeled C (A plus B) rather than only B.

Explanation

Favorable B tiles (5) over the total (16): $\frac{5}{16}$ .

Medium example

A box contains 24 markers: 6 are red, 9 are blue, and 9 are black.

If one marker is selected at random, what is the probability of selecting a marker that is red or blue?

\frac{3}{8}

\frac{1}{2}

\frac{5}{8}

\frac{3}{4}

A: This is the complement — the probability of NOT selecting the target, $\frac{3}{8}$ .

B: This miscounts the favorable outcomes as 4 instead of 5.

C: The probability is the number of favorable outcomes over the total: $\frac{5}{8}$ .

D: This miscounts the favorable outcomes as 6 instead of 5.

Explanation

Red or blue: $6 + 9 = 15$ ; probability $\frac{15}{24} = \frac{5}{8}$ .

Detailed explanation

Red or blue totals $6 + 9 = 15$ out of 24, so the probability is $\frac{15}{24} = \frac{5}{8}$ .

Hard example

A bag contains 30 chips: 6 are red, 9 are blue, and 15 are green.

If 3 of the green chips are removed, what is the probability that a chip selected at random from those remaining is green?

\frac{12}{30}

\frac{12}{27}

\frac{15}{30}

\frac{15}{27}

A: Incorrect. This reduces the green count to 12 but forgets to reduce the total from 30 to 27.

B: Correct. After removing 3 green chips, 12 green remain out of $30 - 3 = 27$ total, so the probability is $\frac{12}{27}$ .

C: Incorrect. This ignores the removal entirely and uses the original 15 green out of 30.

D: Incorrect. This reduces the total to 27 but keeps the original 15 green chips.

Explanation

Green remaining (12) over the new total (27): $\frac{12}{27}$ .

Detailed explanation

Removing 3 green chips lowers both the green count and the total, leaving 12 green out of 27, so the probability is $\frac{12}{27}$ .

The common traps

Pattern	What it does	The tell
Total not updated	Kept the original total after items were removed.	Removing or drawing items changes the total too.
Wrong favorable count	Counted outcomes that do not fit the event.	Match the favorable outcomes exactly to the event.
Part instead of total	Divided by one category rather than the whole group.	The denominator is every possible outcome, not one category.

Try it: two real questions

Question 1easy

A bag contains 20 buttons: 8 are white, 2 are orange, and 10 are brown. If one button is selected at random, what is the probability of selecting a white button?

Question 2easy

A box contains 25 cards: 5 are red, 12 are blue, and 8 are green. If one card is selected at random, what is the probability of selecting a blue card?

Question 3 is ready when you are

Keep going with more questions of this type, each with the same step-by-step reasoning. Free to start.

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Often confused with

Probability & Two-Way Tables

Complement and Total Probability

Probability & Two-Way Tables

Probability from a Two-Way Table

Percentages

Common questions

How do you find a simple probability on the SAT?

Count the favorable outcomes, count the total, and write favorable over total. Simplify or convert to a decimal or percent if the question asks.

What happens to probability when an item is removed?

Both the favorable count and the total can change. Recount the group after the removal, then write the new fraction. Updating only one is the common mistake.

How do I handle drawing without replacement?

After the first draw the item is gone, so the total drops by one and the favorable count drops if that item qualified. Recount both before the second probability.

Is probability a fraction, decimal, or percent on the SAT?

Any of them, depending on the choices. Compute favorable over total first, then convert to the form the question uses.

Practice basic probability the way it is tested

Start with the free 16-question diagnostic, then drill this type with step-by-step reasoning on every question.

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What the question bank shows

How to recognize basic probability questions

Why students miss these

The step-by-step method

Count the favorable outcomes

Count the total outcomes

Write the fraction

Update after a change

Worked examples

The common traps

Try it: two real questions

Question 3 is ready when you are

Often confused with

Related reading

Common questions

How do you find a simple probability on the SAT?

What happens to probability when an item is removed?

How do I handle drawing without replacement?

Is probability a fraction, decimal, or percent on the SAT?

Practice basic probability the way it is tested