Data & Probability · Apply · 4.3

Probability in real life.

Everyday chance — drawing a card, spinning a spinner, picking a name — is simple probability: count the favorable outcomes over the total equally-likely outcomes, then reduce. 5 winning tickets of 12 gives 5/12.

01 / THE IDEA

See it work.

Watch the method

Probability in real life

Real chance → favorable ÷ total, reduced.

1 / 2
A bag of 12 marbles has 5 red. P(red)?
1

Favorable over total

Probability = favorable outcomes ÷ all equally-likely outcomes.

512\frac{5}{12}
2

Simplify

Reduce the fraction to lowest terms.

512=5/12\frac{5}{12} = 5/12
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.

Chance around us

Real-world “what are the odds” questions are favorable ÷ total.

Why it works

Count, then divide.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

A bag of 10 marbles has 6 red. P(red)?

1

Favorable over total

Probability = favorable outcomes ÷ all equally-likely outcomes. 6/10

2

Simplify

Reduce the fraction to lowest terms. 6/10 = 3/5

EX 2medium

A bag of 8 marbles has 7 red. P(red)?

1

Favorable over total

Probability = favorable outcomes ÷ all equally-likely outcomes. 7/8

2

Simplify

Reduce the fraction to lowest terms. 7/8 = 7/8

EX 3hard

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

1

Favorable over total

Probability = favorable outcomes ÷ all equally-likely outcomes. 1/6

2

Simplify

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

04 / COMMON TRAPS

Where students slip.

Trap

Assuming outcomes are equally likely when they aren’t.

Fix

The formula needs equally-likely outcomes.

Trap

Leaving it unreduced.

Fix

Simplify the fraction.

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 11 red. P(red)?

Need a hint?
  • Count favorable outcomes.
  • Divide by all outcomes and reduce.
C2

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

Need a hint?
  • Count favorable outcomes.
  • Divide by all outcomes and reduce.
C3

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

Need a hint?
  • Count favorable outcomes.
  • Divide by all outcomes and reduce.
C4

A bag of 12 marbles has 11 red. P(red)?

Need a hint?
  • Count favorable outcomes.
  • Divide by all outcomes and reduce.
Apply

Apply (4)

A1

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

Need a hint?
  • Count favorable outcomes.
  • Divide by all outcomes and reduce.
A2

A bag of 8 marbles has 7 red. P(red)?

Need a hint?
  • Count favorable outcomes.
  • Divide by all outcomes and reduce.
A3

A bag of 10 marbles has 4 red. P(red)?

Need a hint?
  • Count favorable outcomes.
  • Divide by all outcomes and reduce.
A4

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

Need a hint?
  • Count favorable outcomes.
  • Divide by all outcomes and reduce.
Extension

Extension (4)

E1

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

Need a hint?
  • Count favorable outcomes.
  • Divide by all outcomes and reduce.
E2

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

Need a hint?
  • Count favorable outcomes.
  • Divide by all outcomes and reduce.
E3

A bag of 10 marbles has 8 red. P(red)?

Need a hint?
  • Count favorable outcomes.
  • Divide by all outcomes and reduce.
E4

A bag of 12 marbles has 11 red. P(red)?

Need a hint?
  • Count favorable outcomes.
  • Divide by all outcomes and reduce.