If events A and B are mutually exclusive, write down the value of \({\text{P}} (A\cap B)\).

If events A and B are independent, find the value of \({\text{P}} (A\cap B)\).

If \({\text{P}} (A \cup B) = \frac{7}{13}\), find the value of \({\text{P}} (A \cap B)\).

\({\rm{P}}(A \cap B) = 0\)     (A1)     (C1)

[1 mark]

\({\rm{P}}(A \cap B) = {\rm{P}}(A) \times {\rm{P}}(B)\)

\( = \frac{4}{{13}} \times \frac{5}{{13}}\)     (M1)

Note: Award (M1) for product of two fractions, decimals or percentages.

\({\rm{P}}(A \cap B) = \frac{{20}}{{169}} (= 0.118)\)     (A1)     (C2)

[2 marks]

\(\frac{7}{{13}} = \frac{4}{{13}} + \frac{5}{{13}} - {\rm{P}}(A \cap B)\)     (M1)(M1)

Notes: Award (M1) for \(\frac{4}{{13}} + \frac{5}{{13}}\) seen, (M1) for subtraction of \(\frac{7}{{13}}\) shown.

OR

Award (M1) for Venn diagram with 2 intersecting circles, (A1) for correct probabilities in diagram.

\({\rm{P}}(A \cap B) = \frac{2}{{13}}( = 0.154)\)     (A1)     (C3)

[3 marks]

This question proved to be difficult with many candidates unaware of the significance of mutually exclusive events in probability. A significant number gave the answer to (b) as the answer to (a).

This question proved to be difficult with many candidates unaware of the significance of mutually exclusive events in probability. A significant number gave the answer to (b) as the answer to (a).

This question proved to be difficult with many candidates unaware of the significance of mutually exclusive events in probability.

This part proved to be difficult for some but most of the candidates who used the formula were able to achieve full marks. Very few candidates used Venn diagrams to answer this question.