Probability
Describing and predicting likelihood
Probability tells us how likely something is to happen. We can describe likelihood with words, with proportions ('out of') and with percentages. We can also use likelihood to predict what will happen and to run probability experiments.
The likelihood scale
We can describe how likely an event is using words on a likelihood scale: ā¢ Impossible ā it cannot happen. ā¢ Unlikely ā a small chance. ā¢ Even chance ā just as likely to happen as not. ā¢ Likely ā a good chance. ā¢ Certain ā it will definitely happen.
Probability as a proportion
We can describe likelihood more precisely by counting outcomes. If the outcomes are equally likely, the probability is the number of ways the event can happen 'out of' the total number of outcomes. Example: a bag with 1 yellow, 1 red and 2 green balls has 4 balls, so the probability of green is 2 out of 4.
Using percentages
Probability can also be written as a percentage, which is a proportion out of 100. An even chance is 50%. Example: 2 out of 4 is the same as one half, or 50%. On a weather forecast, a higher percentage means it is more likely to rain.
Mutually exclusive events
Two events are mutually exclusive if they cannot happen at the same time. To check, look for an outcome that fits both events. If there is one, they are not mutually exclusive. If there is no outcome that fits both, they are mutually exclusive.
Predicting outcomes
We can use likelihood to predict how many times something will happen. Work out the proportion for a small number of tries, then scale it up. Example: if a spinner lands on red 4 times in every 8 spins, then in 40 spins (5 lots of 8) you would predict 4 Ć 5 = 20 reds.
Probability experiments
In a probability experiment you carry out trials and record the outcomes in a tally chart. The experimental probability is the number of times an outcome happened out of the total number of trials. The more trials you do, the more clearly the results show the real likelihood of an event.
Worked examples
Describing likelihood with words
- A spinner shows the numbers 1, 2, 3, 4 and 5 ā five equally likely outcomes.
- Only 1 of the 5 numbers is a 5.
- 1 out of 5 is a small chance.
Answer: Spinning a 5 is unlikely.
Probability as a proportion
- A bag holds 1 yellow, 1 red and 2 green balls.
- Count the total number of balls: 4.
- Count how many are green: 2.
Answer: The probability of taking a green ball is 2 out of 4.
Writing a probability as a percentage
- The probability of green is 2 out of 4.
- 2 out of 4 is the same as one half.
- One half written as a percentage is 50%.
Answer: The probability of taking a green ball is 50%.
Mutually exclusive events
- A spinner shows 1, 2, 3, 4 and 5.
- Event A is 'spin a 5' and Event B is 'spin a number less than 4'.
- Check for a number that is both a 5 and less than 4 ā there is none.
Answer: The events cannot happen together, so they are mutually exclusive.
Predicting outcomes
- A spinner is expected to land on red 4 times in every 8 spins.
- 40 spins is 5 lots of 8 spins.
- Multiply the reds by 5: 4 Ć 5.
Answer: You would predict the spinner to land on red 20 times in 40 spins.
Experimental probability
- In a coin experiment, heads came up 24 times and tails 16 times.
- Add them to find the total number of trials: 24 + 16 = 40.
- The experimental probability of tails is 16 out of 40, which is 40%.
Answer: The experimental probability of tails is 40%.
Where you see this in real life
- Reading a percentage chance of rain on a weather forecast to decide whether to take a coat.
- Working out how likely it is to win a toy in a claw machine before deciding to play.
- Predicting how many times a spinner or dice will land on each result in a game.
- Flipping a coin many times to see how close the results get to an even chance.
Key words
- Probability
- How likely something is to happen.
- Outcome
- One of the possible results of an event.
- Event
- Something that may happen, such as spinning a 5.
- Equally likely outcomes
- Outcomes that each have the same chance of happening.
- Mutually exclusive events
- Two events that cannot happen at the same time.
- Probability experiment
- Carrying out trials and recording the outcomes to see how likely an event is.