CAIE S1 2015 June — Question 1 3 marks

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2015
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Distribution
TypeProbability of range of values
DifficultyModerate -0.5 This is a straightforward binomial probability calculation requiring identification of parameters (n=10, p=1/6) and summing P(X=3) + P(X=4) + P(X=5) using the standard formula. While it involves three terms and careful arithmetic, it's a routine textbook exercise with no conceptual challenges beyond applying the binomial distribution formula correctly.
Spec2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities

A fair die is thrown 10 times. Find the probability that the number of sixes obtained is between 3 and 5 inclusive. [3]

Question 1:
AnswerMarks
1P(3, 4, 5) =
3 7 4 6 5
10 1 5 10 1 5 10 1
C3    + C4    + C5 
6 6 6 6 6
5
5
 
6
AnswerMarks
= 0.222M1
A1
AnswerMarks
A1 3Bin expression of form 10 Cx (p) x (1–p) 10–x
any x any p
Correct unsimplified answer accept
(0.17, 0.83), (0.16, 0.84), (0.16, 0.83),
(0.17, 0.84) or more accurate
Correct answer
Question 1:
1 | P(3, 4, 5) =
3 7 4 6 5
10 1 5 10 1 5 10 1
C3    + C4    + C5 
6 6 6 6 6
5
5
 
6
= 0.222 | M1
A1
A1 3 | Bin expression of form 10 Cx (p) x (1–p) 10–x
any x any p
Correct unsimplified answer accept
(0.17, 0.83), (0.16, 0.84), (0.16, 0.83),
(0.17, 0.84) or more accurate
Correct answer
A fair die is thrown 10 times. Find the probability that the number of sixes obtained is between 3 and 5 inclusive. [3]

\hfill \mbox{\textit{CAIE S1 2015 Q1 [3]}}