| Date | May 2018 | Marks available | 2 | Reference code | 18M.2.sl.TZ1.2 |
| Level | SL only | Paper | 2 | Time zone | TZ1 |
| Command term | Find | Question number | 2 | Adapted from | N/A |
Question
A biased four-sided die is rolled. The following table gives the probability of each score.
Find the value of k.
[2]
a.
Calculate the expected value of the score.
[2]
b.
The die is rolled 80 times. On how many rolls would you expect to obtain a three?
[2]
c.
Markscheme
evidence of summing to 1 (M1)
eg 0.28 + k + 1.5 + 0.3 = 1, 0.73 + k = 1
k = 0.27 A1 N2
[2 marks]
a.
correct substitution into formula for E (X) (A1)
eg 1 × 0.28 + 2 × k + 3 × 0.15 + 4 × 0.3
E (X) = 2.47 (exact) A1 N2
[2 marks]
b.
valid approach (M1)
eg np, 80 × 0.15
12 A1 N2
[2 marks]
c.
Examiners report
[N/A]
a.
[N/A]
b.
[N/A]
c.
Syllabus sections
Topic 5 - Statistics and probability » 5.7 » Concept of discrete random variables and their probability distributions.
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