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Date May 2019 Marks available 4 Reference code 19M.2.AHL.TZ1.H_9
Level Additional Higher Level Paper Paper 2 Time zone Time zone 1
Command term Find Question number H_9 Adapted from N/A

Question

A café serves sandwiches and cakes. Each customer will choose one of the following three options; buy only a sandwich, buy only a cake or buy both a sandwich and a cake.

The probability that a customer buys a sandwich is 0.72 and the probability that a customer buys a cake is 0.45.

Find the probability that a customer chosen at random will buy

On a typical day 200 customers come to the café.

It is known that 46 % of the customers who come to the café are male, and that 80 % of these buy a sandwich.

both a sandwich and a cake.

[3]
a.i.

only a sandwich.

[1]
a.ii.

Find the expected number of cakes sold on a typical day.

[1]
b.i.

Find the probability that more than 100 cakes will be sold on a typical day.

[3]
b.ii.

A customer is selected at random. Find the probability that the customer is male and buys a sandwich.

[1]
c.i.

A female customer is selected at random. Find the probability that she buys a sandwich.

[4]
c.ii.

Markscheme

use of formula or Venn diagram       (M1)

0.72 + 0.45 − 1       (A1)

= 0.17       A1

[3 marks]

a.i.

0.72 − 0.17 = 0.55      A1

[1 mark]

a.ii.

200 × 0.45 = 90      A1

[1 mark]

b.i.

let X be the number of customers who order cake

X ~ B(200,0.45)        (M1)

P(X > 100) = P(X ≥ 101)(= 1 − P(X ≤ 100))    (M1)

= 0.0681      A1

 

[3 marks]

b.ii.

0.46 × 0.8 = 0.368    A1

[1 mark]

c.i.

METHOD 1

0.368 + 0.54 × P ( S | F ) = 0.72        M1A1A1 

Note: Award M1 for an appropriate tree diagram. Award M1 for LHS, M1 for RHS.

P ( S | F ) = 0.652      A1  

 

METHOD 2

P ( S | F ) = P ( S F ) P ( F )        (M1)

= 0.72 0.368 0.54        A1A1

Note: Award A1 for numerator, A1 for denominator.

P ( S | F ) = 0.652      A1 

 

[4 marks]

c.ii.

Examiners report

[N/A]
a.i.
[N/A]
a.ii.
[N/A]
b.i.
[N/A]
b.ii.
[N/A]
c.i.
[N/A]
c.ii.

Syllabus sections

Topic 4—Statistics and probability » SL 4.6—Combined, mutually exclusive, conditional, independence, prob diagrams
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Topic 4—Statistics and probability » SL 4.8—Binomial distribution
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