Probability
Probability as favourable outcomes over total outcomes: building the sample space, the complement rule, the addition rule for 'or', the multiplication rule for independent events, and without-replacement problems done by counting.
What you will be able to do
- Write the sample space and count favourable outcomes for a simple experiment.
- Use the complement rule to shortcut an 'at least one' question.
- Apply the addition rule, subtracting the overlap when events are not mutually exclusive.
- Handle without-replacement draws by multiplying the changing fractions or by counting with nCr.
What is inside this lesson
- 1Chance as a number between 0 and 1
- 2Sample space and P(E)
- 3The complement rule
- 4The addition rule for 'or'
- 5Independent events and without-replacement draws
- 6Worked example
- 7Common mistakes
- 8Quick revision
- 9Practice
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Chance as a number between 0 and 1
Probability measures how likely an event is, on a scale from 0 (impossible) to 1 (certain). A probability of 1/2 means the event happens in half of all equally likely outcomes.
Every bank-exam probability question comes down to two counts: how many outcomes are there in total, and how many of them are favourable. Get the counting right — often using the permutation and combination tools from the previous topic — and the probability is just the ratio.
Answers may be left as a fraction in lowest terms or as a decimal; this topic gives decimals to four places where the fraction does not terminate.
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