19M.1.SL.TZ1.S_1

pestleMathematicsAASLPaper 119M· sl-4-6-combined-mutually-exclusive-conditional-independence-prob-diagramssource ↗

The following Venn diagram shows the events $A$ and $B$ , where ${\text{P}}\left( A \right) = 0.3$ . The values shown are probabilities.

Find the value of $p$ .

[2]

Find the value of $q$ .

[2]

Find ${\text{P}}\left( {A' \cup B} \right)$ .

[2]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

valid approach (M1)

eg 0.30 − 0.1, $p$ + 0.1 = 0.3

$p$ = 0.2 A1 N2

[2 marks]

valid approach (M1)

eg 1 − (0.3 + 0.4), 1 − 0.4 − 0.1 − $p$

$q$ = 0.3 A1 N2

[2 marks]

valid approach (M1)

eg $0.7 + 0.5 - 0.3$ , $p + q + 0.4$ , $1 - 0.1$ , ${\text{P}}\left( {A' \cup B} \right) = {\text{P}}\left( {A'} \right) + {\text{P}}\left( B \right) - {\text{P}}\left( {A' \cap B} \right)$

${\text{P}}\left( {A' \cup B} \right) = 0.9$ A1 N2

[2 marks]

Examiners’ report

[N/A]