IB Mathematics Analysis and Approaches Topic SL 4.11—conditional and Independent Probabilities, Test for Independence Questionbank (SL/HL)

IB Mathematics Analysis and Approaches Topic SL 4.11—conditional and Independent Probabilities, Test for Independence Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Analysis and Approaches (AA) Topic SL 4.11—conditional and Independent Probabilities, Test for Independence with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 4.11—conditional and Independent Probabilities, Test for Independence and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

SLPaper 1

Events $A$ and $B$ are such that $P (A) = 0.4$ , $P (B) = 0.7$ and $P (A \cup B) = 0.8$ .

Calculate the value of $P (A \cap B)$ .

[3]

Find the value of $P (A^{'} ∣ B^{'})$ .

[3]

Question 2

SLPaper 1

Events $A$ and $B$ are such that $P (A) = 0.4$ , $P (B) = 0.6$ and $P (A \cup B) = 0.8$ .

Calculate the value of $P (A \cap B)$ .

[3]

Find the value of $P (A^{'} ∣ B^{'})$ .

[3]

Question 3

SLPaper 1

Events $A$ and $B$ are such that $P (A) = 0.7$ , $P (B) = 0.5$ and $P (A \cup B) = 0.9$ .

Calculate the value of $P (A \cap B)$ .

[3]

Find the value of $P (A^{'} ∣ B^{'})$ .

[3]

Question 4

HLPaper 2

A continuous random variable $X$ has probability density function $f (x) = {k x e^{- x /3}, 0, x \geq 0, x < 0.$

Determine the value of the constant $k$ .

[2]

Find $E (X)$ and $Var (X)$ .

[3]

Show that the mode of $X$ is $3$ . Then, by solving $\int_{0}^{m} f (x) d x = \frac{1}{2}$ , find the median $m$ correct to three significant figures (calculator required).

[3]

Let $Y = 2 X + 5$ . Find $E (Y)$ and $Var (Y)$ .

[1]

Compute $P (10 \leq Y \leq 20)$ .

[1]

Find $P (X > 6 ∣ X > 3)$ and give your answer in exact form.

[2]

Question 5

HLPaper 2

A box contains two types of biased coins. One coin is drawn at random and tossed $n = 8$ times.

With probability $0.4$ , a Type A coin is drawn; for Type A, the probability of heads on any toss is $p_{A} = 0.35$ .
With probability $0.6$ , a Type B coin is drawn; for Type B, the probability of heads on any toss is $p_{B} = 0.65$ .

Let $X$ be the total number of heads in the $8$ tosses. Assume tosses are independent conditional on the coin type.

Write down the conditional distributions of $X ∣ A$ and $X ∣ B$ . Hence find $P (X = 3)$ .

[4]

Use the laws of total expectation and total variance to find $E (X)$ and $Var (X)$ .

[5]

The experiment resulted in exactly $6$ heads ( $X = 6$ ). Compute $P (B ∣ X = 6)$ .

[3]

A game pays € $g (x) = 2 x - 9$ . Decide whether to play before observing any tosses.

[2]

After observing that the first two tosses are both heads, you are offered the option to play the game (where the payoff $g (X)$ depends on the total number of heads $X$ in the $8$ tosses). Compute $E [g (X) ∣ first two are heads]$ and decide whether to play.

[4]

IB Mathematics Analysis and Approaches SL 4.11—conditional and Independent Probabilities, Test for Independence Questionbank

IB Mathematics Analysis and Approaches SL 4.11—conditional and Independent Probabilities, Test for Independence Questionbank

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IB Mathematics Analysis and Approaches SL 4.11—conditional and Independent Probabilities, Test for Independence Questionbank

IB Mathematics Analysis and Approaches SL 4.11—conditional and Independent Probabilities, Test for Independence Questionbank

IB Mathematics Analysis and Approaches (AA) Topic SL 4.11—conditional and Independent Probabilities, Test for Independence Questionbank

Unlock all 12 questions with a free account