EXN.1.AHL.TZ0.6

pestleMathematicsAIHLPaper 1EXN· sl-4-6-combined-mutually-exclusive-conditional-independence-prob-diagramssource ↗

The diagram below shows part of the screen from a weather forecasting website showing the data for town $A$ . The percentages on the bottom row represent the likelihood of some rain during the hour leading up to the time given. For example there is a $69 %$ chance (a probability of $0.69$ ) of rain falling on any point in town $A$ between $0900$ and $1000$ .

Paula works at a building site in the area covered by this page of the website from $0900$ to $1700$ . She has lunch from $1300$ to $1400$ .

In the following parts you may assume all probabilities are independent.

Paula needs to work outside between $1000$ and $1300$ and will also spend her lunchtime outside.

Write down the probability it rains during Paula’s lunch break.

[1]

Find the probability it will not rain while Paula is outside.

[2]

Find the probability it will rain at least once while Paula is outside.

[2]

Given it rains at least once while Paula is outside find the probability that it rains during her lunch hour.

[3]

Markscheme / solution

* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.

Note: Accept probabilities written as percentages throughout.

$0.27$ A1

[1 mark]

Note: Accept probabilities written as percentages throughout.

$0.22 \times 0.28 \times 0.52 \times 0.73$ (M1)

$= 0.0234 (0.02338336)$ A1

[2 marks]

Note: Accept probabilities written as percentages throughout.

$1 - 0.02338336$ (M1)

$= 0.977 (0.97661664)$ A1

[2 marks]

Note: Accept probabilities written as percentages throughout.

$P (rains during lunch rains at least once) = \frac{P (r ains during lunch)}{P (rains at least once)}$ M1A1

$\frac{0.27}{0.97661664} = 0.276 (0.276464)$ A1

[3 marks]

Examiners’ report

[N/A]