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Higher June 2017 Unit 2 Q7

WJECHigherCurrent spec5 marksTree Diagrams

7. 100 boxes each contain 10 balls.

45 of the boxes are labelled A.
They each contain 7 black balls and 3 white balls.

25 of the boxes are labelled B.
They each contain 4 black balls and 6 white balls.

The rest of the boxes are labelled C.
They each contain 8 black balls and 2 white balls.

In a game, a player chooses a box at random, and then chooses a ball at random from that box.

(a) Complete the tree diagram shown below. [1]
Tree diagram: Choice of box A (0.45), B (0.25), C (blank); Choice of balls: A Black 0.7, White 0.3; B Black 0.4, White 0.6; C Black 0.8, White 0.2
(b) What is the probability that a player will select a black ball? [3]
(c) If a large number of people played the game, approximately what fraction of them would you expect to choose a white ball?
Circle your answer. [1]

\(\dfrac{1}{10}\)        \(\dfrac{1}{5}\)        \(\dfrac{1}{4}\)        \(\dfrac{1}{3}\)        \(\dfrac{1}{2}\)

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