Equally Likely or Not
List the possible outcomes of chance experiments involving equally likely outcomes and compare to those which are not equally likely.
Read this first
List every outcome first. Then ask if they all have the same chance.
Every number on a die has the same chance.
Words you need
- Outcome
- One thing that could happen.
- Equally likely
- Every outcome has the same chance.
- Sample space
- The list of everything that could happen.
Worked example
e.g. Is spinning a spinner with 3 red parts and 1 blue part equally likely?
- List the outcomes. Red or blue.
- Count the parts. Three are red, one is blue.
- Red covers more of the spinner.
- So they are not equally likely. Red is more likely.
Equal outcomes means equal sized parts, not just two choices.
Practice
The pictures fade as you go. By the last few you are on your own.
1Are the outcomes on a die equally likely?with a picture
AnswerYes. All six faces are the same.
2A bag has 8 red and 2 blue. Equally likely?with a picture
AnswerNo. Red is much more likely.
3List the sample space for tossing a coin.with a hint
Need a hint?
How many sides?
AnswerHead, tail.
4List the sample space for a spinner with 4 equal colours.with a hint
Need a hint?
Name each colour once.
AnswerThe four colours.
5Is tossing a coin equally likely?on your own
AnswerYes. Two sides, both the same.
6A bag has 5 red and 5 blue. Equally likely?on your own
AnswerYes. Same number of each.
7Why is 'red or not red' not always equally likely?on your own
AnswerThere may be far more of one than the other.
Think about it
1
Why list the outcomes first?
One good answerYou cannot judge chances until you know what can happen.
2
Does two choices mean equally likely?
One good answerNo. The parts must be the same size.
Common mistakes
Thinking two outcomes always means a half chance.
Only if both are the same size.
Forgetting an outcome.
List them all before you judge.