MAT-144 · Mathematical Reasoning Topic 06 · Probability
Topic 06 · Review · Q1

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 Worked Example Video

Every step of Probability involving one die or choosing from n distinct objects explained on video. Pause anywhere; the embed scrolls independently of the page.

YOUTUBE
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

A box has 8 cards labeled P, Q, R, S, T, U, V, W. One card is drawn at random. What’s P(letter from P to T)?

Type as a fraction in lowest terms.

P =
Die roll, P(greater than 4)

A fair six-sided die is rolled. What’s P(greater than 4)?

Type as a fraction in lowest terms.

P =
Marbles: blue or green

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

Type as a fraction in lowest terms.

P =
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 The Rule
P(event) = favorable / total count outcomes, divide
Reduce the fraction divide top and bottom by their GCF
Every simple-event probability is one ratio: count the outcomes that satisfy the event (favorable), count all possible outcomes (total), divide. Reduce to lowest terms — ALEKS expects reduced fractions. See it live: P(red) = 4/12 = 1/3 in the Law of Large Numbers Simulator — watch a thousand draws settle onto 1/3 →
Common slips
(1) Off-by-one on ranges. “From P to T” includes both endpoints — P, Q, R, S, T is five cards, not four. (2) Forgot to reduce. 9/12 should become 3/4. ALEKS docks unreduced answers. (3) Wrote a decimal. “As a fraction” means write it as a fraction; 0.375 will be marked wrong.
04 Practice — Step by Step
Practice this problem step by step
A bag contains 4 red, 6 blue, and 2 yellow marbles. One marble is drawn at random. Find P(red) in lowest terms.
Step 1

Count favorable outcomes

How many red marbles are there?
favorable =
Step 2

Count total outcomes

Total marbles in the bag: 4 + 6 + 2.
total =
Step 3

Compute P(red) in lowest terms

P(red) = 4 / 12. Reduce. Type as a fraction (e.g., 1/2).
P(red) =
Topic overview Q2
MAT-144 · TOPIC 06 · REVIEW · Q1 OF 06