Mathematics 0580 · IGCSE · Probability of combined events

Probability of combined events — practice question

A box holds 6 red pencils together with 8 blue pencils. One pencil is selected at random and is not put back. Then a second pencil is selected at random. In the tree diagram, several probabilities have been left blank. The probabilities already shown are $\frac{6}{14}$ for choosing red first and $\frac{8}{13}$ for choosing blue second given that red was chosen first.
(a)[2]

Complete the tree diagram by inserting the missing probabilities.

(b(i))[2]

Calculate the probability that both pencils drawn are red.

(b(ii))[3]

Calculate the probability that at least one of the pencils is red.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Hence, $\frac{8}{14}$ and $\frac{5}{13}$

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