Probability

Learners will be able to... Define the term probability Calculate probability in its simplest form Create a probability scale

What is probability? Write a definition of probability Display a probability in different ways – Words – Low – Numbers and words - 1 in 10 – Fraction - 1/10 – Decimal – Percentage - 10%

Probability The chance or likelihood that an event will happen Certain – definitely going to happen Impossible – it will never happen Likely – to happen Unlikely – to happen Think of something that to fit each category

When do we use probability? Weather reports Gambling – national lottery Passing an exam Statistics

Over to you Decide whether the following are impossible, unlikely or certain. – It will snow on Mount Everest next year – The canteen at college serves food for lunch – You win first prize in a competition – There will be a cure for cancer next year – All the world’s governments will agree to reduce carbon emissions

Example What is the probability that a person chosen at random was born in April? Give your answer as a fraction in its lowest terms. There are 365 days in a year and 30 days in April, so the probability is 30/ 365 = 6/73.

Probability The probability of an event happening and an event not happen should equal 1 or 100%. If the probability it will rain today is 0.4 (40%) then the probability it will not rain will be 0.6 (60%). There is a 60% chance that a football team will win their next match. The probability that they will lose is 30%. What is the probability they will draw their next match?

Measuring probability The probability of an event lies between 0 and 1 Fractions (1/2), percentages (50%) or decimals (0.5) Probability = number of ways the event can happen/total number of possibilities

Example There are 20 female and 12 male students in a psychology group. What is the probability that a student chosen at random will be male? Give your answer as a fraction in its lowest terms. 12/32 3/8

Over to you Card game – in groups True/false or unsure?

Example A survey into train reliability showed that the probability the London to Manchester train was on time was and the probability the train was early was What was the probability the train was late? = – 0.201

Over to you Complete probability with cards handout on moodle Complete probability scale handout on moodle

Experimental Probability Experimental probability is calculated from the results of an experiment. The manufacturing industry uses experimental probability to assess the reliability of their products, so that they can inform their customers and use in advertising.

Example A quality control engineer at Glow-Right Bulbs factory tested 400 bulbs and found 6 bulbs defective. What is the experimental probability that the bulbs are defective? If 6 out of the 400 tested are defective, then you can say: Probability a bulb is defective = 6/400 = 3/ 200 (or as a decimal). The probability can also be expressed as a percentage: 3/ 200 × 100 = 1.5%. This means that in any sample of bulbs, you would expect 1.5% to be defective. Answer 1.5%

Experimental Probability Number of favourable outcomes/number of total outcomes 1/5 is the theoretical probability of landing on a yellow The experimental probability would result in a different answer if spun 10 times.

Experimental probability Using the dice, calculate the experimental probability of the different numbers. OutcomesTallyNo of timesFraction of total

Remember what you have learnt Complete the handout on moodle, print and pass to another learner for marking.