Further Tree Diagrams (AQA A-Level Mathematics): Flashcards

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Further Tree Diagrams
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Effect of 'without replacement' on probabilities

Probabilities update after each draw (denominator and available items decrease)

Total number of discs initially in bag

18 discs (5 red, 6 blue, 7 green)

P(two red discs selected)

10153\frac{10}{153}

P(first disc is red)

518\frac{5}{18}

P(second red | first red already drawn)

417\frac{4}{17}

P(at least one green disc)

96153\frac{96}{153}

P(second green | first blue)

717\frac{7}{17}

Formula for conditional probability P(A|B)

P(A and B)P(B)\frac{P(A \text{ and } B)}{P(B)}

P(first red | second blue)

517\frac{5}{17}

P(second disc is blue)

1751\frac{17}{51}

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