Rensselaer
Electrical, Computer, and Systems Engineering Department
ECSE 4500
Probability for Engineering Applications
PS#1 Solutions
February 12, 2010
1. (1.4) The experiment involves
fl
ipping a fair coin 3 times. The outcome of each coin toss is
either a head or a tail. Therefore, the sample space of the combined experiment that contains
all the possible outcomes of the 3 tosses, is given by
Ω
=
{
HHH, HHT, HTH, HTT, THH, THT, TTH, TTT
}
.
Since all the coins are fair, all the outcomes of the experiment are equally likely. The proba
bility of each singleton event, i.e. an event with a single outcome, is then
1
8
. We are interested
in
fi
nding the probability of the event
A
, which is the event of obtaining 2 heads and 1 tail.
There are 3 favorable outcomes for this event given by
A
=
{
HHT, HTH, THH
}
. Therefore,
P
[
A
] =
P
[
{
HHT
}
∪
{
HTH
}
∪
{
THH
}
] =
P
[
HHT
] +
P
[
HTH
] +
P
[
THH
] =
3
8
. Note that
we are able to write the probability of the event
A
as the sum of probability of the singleton
events (from Axiom 3) because the singlteon events of any experiment are mutually exclusive.
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 Spring '08
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