Question 1

Paper 2, calculatorHard6 marks

A box contains 12 counters, each of which is red or blue. The number of red counters is rr where r∈Zr\in\mathbb{Z} and 1≤r≤111\leq r\leq 11 Two counters are selected successively without replacement.

The probability that the two counters are the same colour is 1733\frac{17}{33}

(a)

Determine the possible values of rr

[2]
(b)

It is also known that the probability that the first counter is red, given that the second counter is red, is 311\frac{3}{11}

(i)

Determine rr

[2]
(ii)

Hence determine the probability that exactly one of the two counters is red.

[2]

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