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Welcome to GCSE Edexcel Maths revision.

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Topic M 36: Probability and experiments.

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This video covers Foundation and Higher tiers.

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A probability lies from 0 to 1 inclusive.

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Impossible events have probability 0; certain events have probability 1.

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A probability of 0.5 describes an even chance.

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The probability scale

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For equally likely outcomes,

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probability of open bracket event close bracket equals the fraction with numerator open bracket number of favourable outcomes close bracket and denominator open bracket total number of possible outcomes close bracket ,

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end fraction .

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Count outcomes rather than assuming every named category is equally likely.

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Worked example: On a fair six-sided die, multiples of 3 are 3 and 6, so their probability is 2 over 6 equals 1 over 3 .

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Fairness means each face has equal probability.

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The probabilities of an exhaustive set of mutually exclusive outcomes sum to 1.

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Exhaustive means all possibilities are covered; mutually exclusive means they cannot happen together.

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For a complementary event, probability of open bracket not A close bracket equals 1 minus probability of open bracket A close bracket .

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If rain has probability 0.3, no rain has probability 0.7 under that model.

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For mutually exclusive events,

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probability of open bracket A or B close bracket equals probability of open bracket A close bracket plus probability of open bracket B close bracket .

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If they overlap, simply adding double-counts the overlap; account for it using a Venn diagram.

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Relative frequency equals the fraction with numerator open bracket number of times the event occurs close bracket and denominator open bracket number of trials close bracket ,

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end fraction .

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This estimates probability from observations; it is not necessarily the exact theoretical value.

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Worked example: A spinner lands on red 38 times in 100 spins.

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Estimated probability of open bracket red close bracket equals 0.38.

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If this model holds, 250 future spins would have about 250 multiplied by 0.38 equals 95 red results.

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Expected frequency equals probability multiplied by number of trials.

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With probability of open bracket success close bracket equals 1 over 4 , 80 trials have expected frequency 20; the actual count can differ.

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More trials usually make an unbiased relative-frequency estimate more reliable.

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It tends towards the theoretical probability for a suitable stable random model, but need not get closer after every extra trial.

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Small samples can give misleading proportions.

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Use a sufficiently large, fair experiment and keep the conditions consistent when estimating future outcomes.

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Independent trials do not balance themselves out on the next trial.

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After five heads on a fair coin, the next toss still has probability of open bracket heads close bracket equals 1 over 2 .

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Frequency tables record counts by outcome.

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A frequency tree splits a total into groups; each parent's count must equal the sum of its branches.

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Counts in a frequency tree

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Worked example: Of 60 students, 35 walk and 25 use transport.

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If 20 walkers and 10 transport users bring lunch, the four leaf counts are 20, 15, 10 and 15.

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They total 60.

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State assumptions such as a fair die, a representative sample or unchanged conditions.

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A mathematically correct calculation can still be an unreliable prediction if its model is inappropriate.

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That completes Probability and experiments.

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Revisit the notes and test yourself on the revision website.