Grade 6 · Count an equally likely event · 217 of 750
Count an equally likely event · practice 20
An equally likely collection has 3 favorable outcomes among 26 total outcomes. Find the event probability and its complement. Follow the calculation, then test the quantities in the animated example.
Try the question, use a hint when you need one, and compare your reasoning with the worked solution. The animation starts with this chapter’s values; changing its controls explores a new case.
01 · Make a prediction
Your practice question
An equally likely collection has 3 favorable outcomes among 26 total outcomes. Find the event probability and its complement.
Use this scratch space or work on paper. Your notes stay on this page and clear when you leave. Answers are for self-checking; they are not automatically graded.
A starting point
Use favorable outcomes over all equally likely outcomes.
Work through the reasoning
Step 1
Translate the givens
Exactly 3 of the 26 outcomes satisfy the event, so P(event) = 3/26.
Step 2
Calculate with the model
Convert to a percent: (3/26) × 100 ≈ 11.53846%.
Step 3
Check and interpret
The other 23 outcomes form the complement. 3/26 + 23/26 = 26/26 = 1.
The answer
P(event) = 3/26 ≈ 11.53846%; P(complement) = 23/26.
Compare the method as well as the result. A different valid method may reach the same answer. Keep exact values until the last step when the question asks for rounding.
02 · Explore the model
See the mathematical relationship move.
Use Play, Pause, and the timeline to inspect the construction. Reset restores the question’s original settings. The displayed assumptions describe where this model applies.
Watch the relationship
PausedHD animation studio
From experiment to screen.
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The mathematical idea
For a finite collection of equally likely outcomes, a probability is the fraction that satisfy the event. Counting favorable outcomes is not enough without naming the full sample space. The scanning marker inspects known outcomes and is not a random experiment. Starting quantities: Favorable outcomes = 3; Total equally likely outcomes = 26.
P(event) = favorable outcomes / total outcomes
03 · Reflect and transfer
Explain what changes and why.
Why would this count ratio be insufficient if the outcomes were not equally likely?
This is a distinct guided scenario using a reusable mathematical model. Similar-looking diagrams can represent different given values and conclusions; they are not different mathematical theories.