User interface language: English | Español

Date November 2020 Marks available 2 Reference code 20N.2.SL.TZ0.T_2
Level Standard Level Paper Paper 2 Time zone Time zone 0
Command term Find Question number T_2 Adapted from N/A

Question

On a school excursion, 100 students visited an amusement park. The amusement park’s main attractions are rollercoasters (R), water slides (W), and virtual reality rides (V).

The students were asked which main attractions they visited. The results are shown in the Venn diagram.

A total of 74 students visited the rollercoasters or the water slides.

Find the value of a.

[2]
a.i.

Find the value of b.

[2]
a.ii.

Find the number of students who visited at least two types of main attraction.

[2]
b.

Write down the value of n( RW) .

[1]
c.

Find the probability that a randomly selected student visited the rollercoasters.

[2]
d.i.

Find the probability that a randomly selected student visited the virtual reality rides.

[1]
d.ii.

Hence determine whether the events in parts (d)(i) and (d)(ii) are independent. Justify your reasoning. 

[2]
e.

Markscheme

74-32+12+10+9+5  OR  74-68     (M1)


Note: Award (M1) for setting up a correct expression.


a=  6       (A1)(G2)


[2 marks]

a.i.

100-74+18     (M1)

OR

100-92     (M1)

OR

100-32+9+5+12+10+18+6     (M1)


Note:
Award (M1) for setting up a correct expression. Follow through from part (a)(i) but only for a0.


b=  8       (A1)(ft)(G2)


Note:
Follow through from part(a)(i). The value of b must be greater or equal to zero for the (A1)(ft) to be awarded.


[2 marks]

a.ii.

9+5+12+10     (M1)


Note:
Award (M1) for adding 9, 5, 12 and 10.


36       (A1)(G2)


[2 marks]

b.

14     (A1)

[1 mark]

c.

58100  2950, 0.58, 58%     (A1)(A1)(G2)


Note: Award (A1) for correct numerator. Award(A1) for the correct denominator. Award (A0) for 58 only.


[2 marks]

d.i.

45100  920, 0.45, 45%     (A1)(ft)


Note: Follow through from their denominator from part (d)(i).


[1 mark]

d.ii.

they are not independent     (A1)(ft)

58100×4510017100  OR  0.2610.17     (R1)


Note: Comparison of numerical values must be seen for (R1) to be awarded.
Do not award (A1)(R0). Follow through from parts (d)(i) and (d)(ii).


[2 marks]

e.

Examiners report

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

Syllabus sections

Topic 4—Statistics and probability » SL 4.6—Combined, mutually exclusive, conditional, independence, prob diagrams
Show 306 related questions
Topic 4—Statistics and probability

View options