Mathematics 4024 · O Level · Probability of combined events

Probability of combined events — practice question

Inside a bag there are twelve lettered tiles that spell TRIGONOMETRY.
(a)[1]

A tile is drawn at random from the bag. Find the probability that the tile shows a letter R. Give your answer as a fraction in its simplest form.

(b)[2]

All the tiles are returned to the bag. One tile is then drawn at random and placed on the table. A second tile is drawn at random and placed to the right of the first tile. A third tile is drawn at random and placed to the right of the second tile. Find the probability that, in the order the tiles were placed on the table, they spell GET.

(c(i))[2]

Vowels are the letters A, E, I, O and U. Every other letter is a consonant. All twelve tiles are put back in the bag and two tiles are then drawn at random, without replacement. Complete the tree diagram.

(c(ii))[1]

Find the probability that both tiles show vowels.

(c(iii))[2]

Find the probability that one tile shows a vowel and the other shows a consonant.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Hence the probability is $\frac{1}{6}$.

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