Foundation November 2021 Paper 3 Q11

AQACurrent spec4 marksBasic Probability

11 In a game, the player going first uses crosses and the player going second uses circles.

To win the game, a player must get three crosses or three circles together in a line.

The line must be horizontal, vertical or diagonal.

(a) Here is the position in a game.
A 6 by 6 grid with columns A to F and rows 1 to 6. Circles in E1, D2, B5 and E5. Crosses in C3, D3, D4 and B6

It is Amy’s turn to put a cross on the grid.

She wins if she puts a cross in B3

Write down all the other squares where she could put a cross to win the game. [2 marks]

(b) Amy goes first in the next game.
An empty 6 by 6 grid with columns A to F and rows 1 to 6

Assume that she will choose a square at random.

Write down the probability that she will put her first cross in square F6 [1 mark]

(c) In fact, Amy decides to put her first cross into a corner square.

What does this mean about the probability that she will put her first cross in square F6?

Tick a box.

  • It is smaller than the answer to part (b)
  • It is greater than the answer to part (b)
  • It is the same as the answer to part (b)

Give a reason for your answer. [1 mark]

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