MAI HL
Test on Descriptive Statistics and Probability
by Christos Nikolaidis
Date: 2 March 2021
Marks:
/60
Name of student: __________________________________________________
1.
[Maximum mark: 6]
In a group of 20 girls, 13 take history and 8 take economics. Three girls take both
history and economics.
(a)
Complete a Venn diagram to represent the information.
(b)
A girl is selected at random. Find the probability that she takes economics but
not history.
(c)
[2]
Given that the girl does not take history, find the probability that she takes
economics.
2.
[2]
[2]
[Maximum mark: 6]
Consider the following table.
Find
3.
(a)
The mode and the mean.
[2]
(b)
The range and the interquartile range.
[2]
(c)
The variance.
[2]
[Maximum mark: 4]
The mean of four integers is 8, the mode is 10 and the median is 9. Find the four
integers.
1
4.
[Maximum mark: 8]
(c)
5.
Determine whether the two events A and B are independent or not.
[2]
[Maximum mark: 10]
(c)
Another athlete on this sport team has a height of 180 cm. Estimate the hand
length of this athlete correct to 2 dp
6.
(i)
by using the regression line of y on x
(ii)
by using the regression line of x on y.
[4]
[Maximum mark: 6]
For two independent events A and B, P(A) = 0.2 and P(A B) = 0.76.
7.
(a)
Write down P(A|B).
[2]
(b)
Find P(B).
[4]
[Maximum mark: 7]
A box contains 10 black balls and 2 red balls.
(a)
Two balls are selected at random without replacement. Find the probability
that the two balls are of different colors.
(b)
Three balls are selected at random with replacement. Find the probability
that all three balls are black.
(c)
[3]
[2]
Three balls are selected at random without replacement. Find the probability
that all three balls are black.
[2]
2
8.
[Maximum mark: 8]
(a)
Complete a tree diagram to represent this information.
[2]
(b)
Find the probability that Pablo leaves home before 07:00 and is late for work.
[2]
(c)
Find the probability that Pablo is late for work.
[2]
(d)
Given that Pablo is late for work, find the probability that he left home
before 07:00.
9.
[2]
[Maximum mark: 5]
Box A contains 5 red and 3 green balls. Box B contains 4 red and 5 green balls.
A ball is selected at random from box A and moved into box B. Then a ball is
selected at random from box B. Find the probability that the second ball is green.
3