Class 10 Maths · Chapter 14 · Topic 1 of 9
Check what is equally likely
Identify equally likely elementary outcomes before counting.
Ideas you’ll use
- Equally likely outcomes
- Outcomes with the same chance under the stated model. A fair coin has two equally likely face outcomes; a fair ordinary die has six.
Understand it, one idea at a time
Choose an idea. Follow its reason, calculation and clue in the picture.
Five orange outcomes and two blue outcomes
- Counting unit
- One token, not one colour label.
- Assumption
- Uniform draw from thoroughly mixed identical-size tokens.
Choose the actual outcomes
A bag with five orange and two blue tokens has seven individual-token outcomes.
O1,…,O5,B1,B2In the picture: Each token has a place in the sample space.
Read all the reasoning together
Choose the actual outcomes
A bag with five orange and two blue tokens has seven individual-token outcomes.
O1,…,O5,B1,B2State the model’s assumption
A uniform draw makes each token equally likely, not each colour.
P(each token)=1/7Count the event’s tokens
Orange has five outcomes and blue has two.
P(orange)=5/7; P(blue)=2/7Do not assume equal chances from two labels
A machine working or failing has two possibilities, but no automatic 1/2 probability.
Two event names ≠ equally likely outcomes
Identify equally likely elementary outcomes before counting.
Worked example: An original token model
P(orange)=5/7; P(blue)=2/7Count individual tokens, not colour names, in the denominator. Random selection must make each token equally likely; identical size and thorough mixing support that model.
Read the supporting explanation
A machine can work or fail, but those two events need not have equal probabilities. A bag with five orange tokens and two blue tokens gives seven equally likely individual-token outcomes if each is selected uniformly; the two colours are not equally likely.
Go deeper: Outcome versus event
An outcome is one possible result. An event is a set of outcomes satisfying a condition. An elementary event contains one outcome. The event “even die result” contains 2, 4, 6, so it is not elementary.
Your turn
Try the idea yourself. Show your reasoning, then compare.
Question
A spinner has two colours covering different-sized regions. Can each colour be assigned 1/2 just because there are two colours?
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