Mathematics HL
STATISTICS & PROBABILITY
Worksheet 1
1.
No GDC
Consider the data set {
k
− 2,
k
,
k
+1,
k
+ 4}, where
k
.
(a)
Find the mean of this data set in terms of
k
.
(3)
Each number in the above data set is now
decreased
by 3.
(b)
Find the mean of this
new
data set in terms of
k
.
(2)
(Total 5 marks)
2.
Events
A
and
B
are such that P(
A
) = 0.3 and P(
B
) = 0.4.
(a)
Find the value of P(
A
B
) when
(i)
A
and
B
are mutually exclusive;
(ii)
A
and
B
are independent.
(4)
(b)
Given that P(
A
B
) = 0.6, find P(
A

B
)
.
(3)
(Total 7 marks)
3.
In a population of rabbits, 1 % are known to have a particular disease. A test is developed
for the disease that gives a positive result for a rabbit that
does
have the disease in 99 %
of cases. It is also known that the test gives a positive result for a rabbit that
does not
have the disease in 0.1 % of cases. A rabbit is chosen at random from the population.
(a)
Find the probability that the rabbit tests positive for the disease.
(2)
(b)
Given that the rabbit tests positive for the disease, show that the probability that
the rabbit does not have the disease is less than 10 %.
(3)
(Total 5 marks)
4.
The random variable
X
has probability density function
f
where
f
(
x
) =
(a)
Sketch the graph of the function. You are not required to find the coordinates of
the maximum.
(1)
(b)
Find the value of
k.
(5)
(Total 6 marks)
5.
A continuous random variable
X
has a probability density function given by the function
f
(
x
), where
f
(
x
) =
(a)
Find the value of
k.
(2)
−
+
otherwise.
,
0
2
0
),
2
)(
1
(
x
x
x
kx
−
+
otherwise.
,
0
3
4
0
,
0
2
)
2
(
2
x
k
x
x
k