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.

Paper

Paper 1, no calculator Paper 2, calculator

Difficulty

Easy Medium Hard

Question 1

Paper 2, calculatorEasy5 marks

A student uses the spinner shown in Figure 1. Each of its six sectors is equally likely to be selected. Let $A$ be the event that the spinner lands on a number greater than $4$

(a)

List the outcomes in $A$

[1]

(b)

Determine $P(A)$

[1]

(c)

State $P(A')$ where $A'$ is the complement of $A$

[1]

(d)

Determine the expected number of times the spinner lands on a number greater than $4$ in $30$ spins.

[1]

(e)

In a separate trial of $30$ spins, the spinner lands on a number greater than $4$ eight times. Calculate the relative frequency of $A$

[1]

Question 2

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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