Data & Probability · Probability · 3.1

Simple probability.

Probability measures how likely an event is: the number of favorable outcomes divided by the total number of equally-likely outcomes, written as a fraction. 3 red marbles out of 8 gives P(red) = 3/8.

01 / THE IDEA

See it work.

Watch the method

Simple probability

P(event) = favorable ÷ total (reduced).

1 / 2
A bag of 8 marbles has 3 red. P(red)?
1

Favorable over total

Probability = favorable outcomes ÷ all equally-likely outcomes.

38\frac{3}{8}
2

Simplify

Reduce the fraction to lowest terms.

38=3/8\frac{3}{8} = 3/8
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type the answer as a fraction, decimal, or percent (e.g. 1/4, 0.25, 25%).

streak 0
best 0

…

— / WHY IT WORKS

The idea underneath.

Count the ways

List the favorable outcomes over all the equally-likely ones.

Why it works

Wanted ÷ possible.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

A bag of 6 marbles has 3 red. P(red)?

1

Favorable over total

Probability = favorable outcomes ÷ all equally-likely outcomes. 3/6

2

Simplify

Reduce the fraction to lowest terms. 3/6 = 1/2

EX 2medium

A bag of 8 marbles has 6 red. P(red)?

1

Favorable over total

Probability = favorable outcomes ÷ all equally-likely outcomes. 6/8

2

Simplify

Reduce the fraction to lowest terms. 6/8 = 3/4

EX 3hard

A bag of 6 marbles has 3 red. P(red)?

1

Favorable over total

Probability = favorable outcomes ÷ all equally-likely outcomes. 3/6

2

Simplify

Reduce the fraction to lowest terms. 3/6 = 1/2

04 / COMMON TRAPS

Where students slip.

Trap

Using favorable over favorable.

Fix

Denominator is ALL outcomes, not just the wanted ones.

Trap

Leaving it unreduced.

Fix

Simplify the fraction to lowest terms.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

A bag of 12 marbles has 1 red. P(red)?

Need a hint?
  • Count favorable outcomes.
  • Divide by the total outcomes.
C2

A bag of 8 marbles has 6 red. P(red)?

Need a hint?
  • Count favorable outcomes.
  • Divide by the total outcomes.
C3

A bag of 6 marbles has 4 red. P(red)?

Need a hint?
  • Count favorable outcomes.
  • Divide by the total outcomes.
C4

A bag of 12 marbles has 10 red. P(red)?

Need a hint?
  • Count favorable outcomes.
  • Divide by the total outcomes.
Apply

Apply (4)

A1

A bag of 8 marbles has 5 red. P(red)?

Need a hint?
  • Count favorable outcomes.
  • Divide by the total outcomes.
A2

A bag of 8 marbles has 1 red. P(red)?

Need a hint?
  • Count favorable outcomes.
  • Divide by the total outcomes.
A3

A bag of 12 marbles has 2 red. P(red)?

Need a hint?
  • Count favorable outcomes.
  • Divide by the total outcomes.
A4

A bag of 8 marbles has 4 red. P(red)?

Need a hint?
  • Count favorable outcomes.
  • Divide by the total outcomes.
Extension

Extension (4)

E1

A bag of 6 marbles has 1 red. P(red)?

Need a hint?
  • Count favorable outcomes.
  • Divide by the total outcomes.
E2

A bag of 10 marbles has 9 red. P(red)?

Need a hint?
  • Count favorable outcomes.
  • Divide by the total outcomes.
E3

A bag of 12 marbles has 1 red. P(red)?

Need a hint?
  • Count favorable outcomes.
  • Divide by the total outcomes.
E4

A bag of 6 marbles has 3 red. P(red)?

Need a hint?
  • Count favorable outcomes.
  • Divide by the total outcomes.