Probability

Probability

Secondary 4

A fair coin determines which box is used.

Head : choose Box X, containing \(4\) red counters and \(1\) blue counter.
Tail : choose Box Y, containing \(1\) red counter and \(4\) blue counters.

Two counters are then selected from the chosen box without replacement.

  1. Draw the relevant tree branches and calculate the probability that both counters are red.

  2. Find the overall probability that the first counter is red.

  3. Suppose you are told only that the first counter was red. Find the probability that the second counter is red by comparing the relevant path probabilities.

  4. Are “first counter is red” and “second counter is red” independent? Justify your answer.

Solution:

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Answer:(a) \(\frac{3}{10}\); (b) \(\frac{1}{2}\); (c) \(\frac{3}{5}\); (d) Dependent.

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