IB Maths AA SL AA 4.3 Probability questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

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Question 1

Paper 2, calculatorHard6 marks

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

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

(a)

Determine the possible values of $r$

[2]

(b)

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

(i)

Determine $r$

[2]

(ii)

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

[2]

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