User interface language: English | Español

Date May 2016 Marks available 3 Reference code 16M.1.sl.TZ1.2
Level SL only Paper 1 Time zone TZ1
Command term Find Question number 2 Adapted from N/A

Question

The following Venn diagram shows the events \(A\) and \(B\), where \({\text{P}}(A) = 0.4,{\text{ P}}(A \cup B) = 0.8\) and \({\text{P}}(A \cap B) = 0.1\). The values \(p\) and \(q\) are probabilities.

M16/5/MATME/SP1/ENG/TZ1/02

(i)     Write down the value of \(q\).

(ii)     Find the value of \(p\).

[3]
a.

Find \({\text{P}}(B)\).

[3]
b.

Markscheme

(i)     \(q = 0.1\)     A1     N1

(ii)     appropriate approach     (M1)

eg\(\,\,\,\,\,\)\({\text{P}}(A) - q,{\text{ }}0.4 - 0.1\)

\(p = 0.3\)    A1     N2

[3 marks]

a.

valid approach     (M1)

eg \(\,\,\,\,\,\)\({\text{P}}(A \cup B) = {\text{P}}(A) + {\text{P}}(B) - {\text{P}}(A \cap B),{\text{ P}}(A \cap B) + {\text{P}}(B \cap A')\)

correct values     (A1)

eg\(\,\,\,\,\,\)\(0.8 = 0.4 + {\text{P}}(B) - 0.1,{\text{ }}0.1 + 0.4\)

\({\text{P}}(B) = 0.5\)    A1     N2

[3 marks]

b.

Examiners report

This question was well done by most candidates. In part (b), the intersection \({\text{P}}(A \cap B)\) was sometimes overlooked, incorrectly using \({\text{P}}(A \cup B) = {\text{P}}(A) + {\text{P}}(B)\) instead.

a.

This question was well done by most candidates. In part (b), the intersection \({\text{P}}(A \cap B)\) was sometimes overlooked, incorrectly using \({\text{P}}(A \cup B) = {\text{P}}(A) + {\text{P}}(B)\) instead.

b.

Syllabus sections

Topic 5 - Statistics and probability » 5.5
Show 78 related questions

View options