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Year 8 Mathematics

Probability

Probability

• Learning Intentions– Understand the terms: experiment, outcome,

event, probability and equally likely– place events in order of likelihood – understand the probability scale– understand why repeating the same experiment

does not always give the same result– calculate the probability of an event occurring

Key Terms

• If you roll an ordinary die, there are 6 possible outcomes

• The act of rolling the die is called an experiment or trial

• The score you get is called an outcome or an event

• The list 1, 2, 3, 4, 5 and 6 are the possible outcomes

The Probability Scale

• Probability is a measure of how likely an event is to happen

• Maths uses numbers to describe probabilities• Probabilities can be written as fractions,

decimals or percentages• You can also use a probability scale, starting at

0 (impossible) and ending at 1 (certain).

Calculating Probability

• If all the outcomes of an experiment are equally likely, then the probability of an event A happening is given by this formula

• For example the probability of tossing a coin an getting a head is– P(Head) =

21

Calculating Probability

• If there is more than one possibility of an outcome occurring, the probability of selecting that outcome is increased

• The probability of selecting a red counter from a bag containing two red counters, one green counter and one yellow counter is

• P(red) = =42

21

Experimental Probability

• When an experiment is carried out the number of outcomes are not the same each time

• If you roll a die 60 times, sometimes you might get 9 twos and sometimes you might get 12 twos

• We calculate the experimental probability as:– P(outcome) = sexperimentof number

successesof number

Expected Outcomes

• If an experiment is repeated the expected number of outcomes can be calculated from the probability

• For example:– If you roll a die 60 times, we would expect to roll a

two, of the times– We would expect to get x 60 = 10 twos– No of Outcomes = P(outcome) x no of experiments

61

61

Bias

• Bias occurs when one outcome regularly occurs more often than another

• For example: – if we roll a die 60 times we would expect there to

be 10 sixes– If we get 20 sixes we would expect the die to be

biased– The die could be heavier on the side opposite

the six