Probability involving one die or choosing from n distinct objects

Count the favorable outcomes, count the total in the sample space, divide, reduce. The most basic probability move on the test.

01 Mini-Lesson Video

▸ VIDEO COMING SOON

A short walkthrough explaining what you need to know and how to solve this question type lands here once it's recorded.

02 What This Looks Like on ALEKS

ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here are three example versions you might see.

Box of 8 cards v1

A box contains eight cards labeled P, Q, R, S, T, U, V, and W. One card will be randomly chosen. What is the probability of choosing a letter from P to T?

Write your answer as a fraction.

Die roll, P(greater than 4) v2

A fair six-sided die is rolled. What is the probability of rolling a number greater than 4?

Write your answer as a fraction.

Marbles in a bag v3

A bag contains 3 red, 5 blue, and 4 green marbles. One marble is drawn at random. What is P(blue or green)?

Write your answer as a fraction in lowest terms.

Heads up: Your ALEKS version will use different numbers. The numbers in the practice below are different too — that way you're exercising the move, not memorizing one answer.

03 How to Solve It

P(event) = favorable outcomes / total outcomes
reduce the fraction when possible

Every simple-event probability is one ratio. List the favorable outcomes, count the total, divide.

List the sample space.

Eight cards: {P, Q, R, S, T, U, V, W}. Total outcomes = 8.

Count favorable outcomes.

"A letter from P to T" includes P, Q, R, S, T — five cards.

favorable = 5

Build the ratio and reduce.

P(P to T) = 5 / 8 = 5/8

5 and 8 share no common factors (5 is prime; 8 = 2³), so 5/8 is already in lowest terms.

▸ COMMON SLIPS(1) Counted P to T as 4. Both endpoints are included — P, Q, R, S, T is five cards, not four. (2) Forgot to reduce. When the fraction has a common factor in numerator and denominator, divide it out. ALEKS expects lowest terms. (3) Wrote the answer as a decimal. The prompt explicitly says "as a fraction." 0.625 will be marked wrong.

04 Practice — Step by Step

Try two more. Same recipe: count favorable, count total, divide, reduce.

Roll the die.

A fair six-sided die is rolled. What is P(greater than 4)? Fraction in lowest terms.

P =

Draw a marble.

A bag has 3 red, 5 blue, and 4 green marbles. What is P(blue or green)? Fraction in lowest terms.

P =

▸ NICE WORK

You've walked through the whole problem.

That's the move. ALEKS will give you a different version with different numbers — but the steps are the same.

Topic overview Q2