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Question id: 145. This question is similar to one that appeared in a GCSE Higher paper (specimen) for 2017. The use of a calculator is allowed.

### Probability

Derren thinks he is a mind reader and can tell what Paige is thinking. An experiment was conducted to test this.

Derren and Paige sit either side of a screen and Paige rolls a six-sided fair dice. Paige then thinks about the number on the dice while Derren tries to predict this number.

(a) In 900 attempts, how many correct predictions would you expect Derren to make if he was just guessing?

The results of the first 15 attempts are shown in the table:

 Paige's Number 4 6 3 3 3 2 2 2 3 1 1 5 1 1 2 Derren's Guess 1 2 2 4 2 2 1 4 2 4 2 6 1 2 2 Guess Correct ✓ ✓ ✓

(b) Estimate the probability of getting a matching pair using the results of the last five guesses.

(c) Estimate the probability of getting a matching pair using all 15 results.

(d) Use this information to comment on Derrenâ€™s belief that he knows what Paige is thinking.

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