Page 1 of 4
The Hong Kong University of Science and Technology
ISMT 111  Business statistics, Fall 2002
Problem Sheet 2
Solutions
1.
Let
A
and
B
be the event that
A
 Employee favors a buyout
B
 Employee will retire within the next 15 years
(a) P(
A
) = 0.382
(b) P(
B
) = 0.379
(c) P(
AB
) = 0.55
(d)
Since P(
A

B
)
≠
P(
A
), the two events
A
and
B
are dependent. In other words, an employee’s attitude
towards the buyout is dependent on his or her retirement plan.
2.
(a) Let
T
be the event that the chosen coin is twoheaded
P(
T
) = 1/10 = 0.1
(b)
Let T be the event that the chosen coin is twoheaded and
X be the number of heads obtained in 3 trials.
Pr(
X =
1) = 0.3375
(c)
Probability of getting 2 heads from the coin tossing experiment:
Pr(
X =
2) = 0.3375
(d)
Probability distribution for the number of heads obtained from the experiment.
Pr(
X =
0) = 0.1125
Pr(
X =
3) = 0.2125
The distribution of
X
is given by
x
0
1
2
3
P(x)
0.1125
0.3375
0.3375
0.2125
(e)
Mean and Standard deviation of the above distribution:
μ
= 1.65,
s
= 0.9367
(f)
Probability that the chosen coin is twoheaded, given the results of the experiment are all heads: Pr(
T

X =
3) = 0.4706
(g)
If the chosen coin is tossed a million times and the result are all heads,
1
)
1000000

Pr(
=
=
X
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 Spring '09
 AnthonyChan

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