Probability: how convinced are we? — Mathematics, 11–13
A probability tells how strongly we believe something will happen, from 0% to 100%, and it can be estimated with a relative frequency.
A degree of belief from 0% to 100%
The probability of an event tells how convinced we are that it will happen. It goes from 0% to 100%: 0% is an impossible event, 100% is a certain one, and 50% is halfway, as likely as not. It is never negative and never above 100%. “There is a 90% probability of rain” says we are almost sure; “10%” says we are hardly convinced at all. You can mark probabilities on a line from 0% to 100%.
Preparing for what is uncertain
The future is uncertain, but it is not a total mystery: probabilities help us prepare. A 90% chance of rain calls for an umbrella; 10% probably does not. To put a number on a probability we often look at what has already happened and see in which fraction of the tries the event occurred. That fraction is the relative frequency, and it is our estimate of the probability.
Estimating with a bottle cap
You want to estimate the probability that a bottle cap lands with its open side up. You toss it 50 times and it lands that way 18 times. Step 1: relative frequency = times it happened ÷ number of tries = 18/50. Step 2: 18/50 = 36/100 = 36%. Estimate: about 36%. On the line from 0% to 100% it sits below 50%: landing open side up is less likely than not. It is an estimate, not a certainty: another 50 tosses may give a slightly different value.
What holds for one group may not hold for another
In three 5th-year classes of 25 pupils, 15, 16 and 14 pupils have a pet: 60%, 64% and 56%, and 45 out of 75, which is 60%, all together. For a fourth 5th-year class you can conjecture a value near 60%. But for a group of adults, or of pupils in a very different place, you cannot just copy it: the group is different, and the number may be too. To trust the conjecture, check it with data from that group.
Weather, canteens, games: predicting the uncertain
When you hear “there is a 70% probability of rain”, you see probabilities at work: it is not a certainty, but it is enough to decide to take an umbrella. A canteen can estimate how many pupils will ask for the vegetarian menu from the relative frequency of previous days. Mathematics does not tell the future, but it helps us to be better prepared for what is uncertain, and to understand the world with numbers.
Keep exploring
Other languages
Loading MyLeoNes™…