SPM.1.SL.TZ0.2

pestleMathematicsAASLPaper 1SPM· sl-4-6-combined-mutually-exclusive-conditional-independence-prob-diagramssource ↗

Let A and B be events such that ${\text{P}}\left( A \right) = 0.5$ , ${\text{P}}\left( B \right) = 0.4$ and ${\text{P}}\left( {A \cup B} \right) = 0.6$ .

Find ${\text{P}}\left( {\left. {A\,} \right|B} \right)$ .

Markscheme / solution

attempt to substitute into ${\text{P}}\left( {A \cup B} \right) = {\text{P}}\left( A \right) + {\text{P}}\left( B \right) - {\text{P}}\left( {A \cap B} \right)$ (M1)

Note: Accept use of Venn diagram or other valid method.

$0.6 = 0.5 + 0.4 - {\text{P}}\left( {A \cap B} \right)$ (A1)

${\text{P}}\left( {A \cap B} \right) = 0.3$ (seen anywhere) A1

attempt to substitute into ${\text{P}}\left( {\left. {A\,} \right|B} \right) = \frac{{{\text{P}}\left( {A \cap B} \right)}}{{{\text{P}}\left( B \right)}}$ (M1)

$= \frac{{0.3}}{{0.4}}$

${\text{P}}\left( {\left. {A\,} \right|B} \right) = 0.75\left( { = \frac{3}{4}} \right)$ A1

[5 marks]

Examiners’ report

[N/A]