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Probability with Tree Diagrams

≈ 25 min
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The probability of an event is

P(event)=number of favourable outcomestotal number of outcomesP(\text{event}) = \frac{\text{number of favourable outcomes}}{\text{total number of outcomes}}

always a value between 0 (impossible) and 1 (certain). For a fair coin, P(heads)=12P(\text{heads}) = \tfrac{1}{2}.

A tree diagram organises a two-stage experiment. Each stage branches into its possible outcomes, and following a path from start to tip gives one combined outcome.

Worked example — two coin tosses. The first toss branches into H and T; each of those branches again into H and T, giving four equally likely paths: HH, HT, TH, TT. To get the probability along a path, multiply the branch probabilities: P(HH)=12×12=14P(\text{HH}) = \tfrac12 \times \tfrac12 = \tfrac14. For an event covering several paths, add those paths' probabilities.

A fair coin is tossed once. What is the probability of getting heads? Give your answer as a decimal.

A fair coin is tossed twice. What is the probability of getting two heads (HH)? Give your answer as a decimal.

To find the probability of a single combined outcome by following one path of a tree diagram, you…

A fair coin is tossed twice. What is the probability of getting at least one head? Give your answer as a decimal.