21N.1.SL.TZ0.4

pestleMathematicsAASLPaper 121N· sl-4-6-combined-mutually-exclusive-conditional-independence-prob-diagramssource ↗

Box 1 contains 5 red balls and 2 white balls.

Box 2 contains 4 red balls and 3 white balls.

A box is chosen at random and a ball is drawn. Find the probability that the ball is red.

[3]

Let $A$ be the event that “box 1 is chosen” and let $R$ be the event that “a red ball is drawn”.

Determine whether events $A$ and $R$ are independent.

[2]

Markscheme / solution

valid approach to find $P (R)$ (M1)

tree diagram (must include probabilty of picking box) with correct required probabilities

OR $P (R \cap B_{1}) + P (R \cap B_{2})$ OR $P (R B_{1}) P (B_{1}) + P (R B_{2}) P (B_{2})$

$\frac{5}{7} \cdot \frac{1}{2} + \frac{4}{7} \cdot \frac{1}{2}$ (A1)

$P (R) = \frac{9}{14}$ A1

[3 marks]

events $A$ and $R$ are not independent, since $\frac{9}{14} \cdot \frac{1}{2} \neq \frac{5}{14}$ OR $\frac{5}{7} \neq \frac{9}{14}$ OR $\frac{5}{9} \neq \frac{1}{2}$

OR an explanation e.g. different number of red balls in each box A2

Note: Both conclusion and reasoning are required. Do not split the A2.

[2 marks]

Examiners’ report

[N/A]