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Probability distributions 83
Socialists win
0.6
Assets nationalized
Assets not nationalized
Conservatives win Assets not nationalized
0.4
Figure 4.1 – A probability tree
0.8
0.2
0.3
Assets nationalized
0.7
0.6 × 0.8 = 0.48
+
0.4 × 0.3 = 0.12
p(assets nationalized) =
We then determine the probability that the Conservatives will win
and that the assets will be nationalized:
p(Conservatives win and assets nationalized)
= p(Conservatives win) × p(assets nationalized|Conservatives win)
= 0.4 × 0.3 = 0.12
Now we can obtain the overall probability of the assets being nationalized
as follows:
p(assets nationalized) = p(either Socialists win and nationalize or
Conservatives win and nationalize)
These two events are mutually exclusive, since we assume that the
election of one party precludes the election of the other, so we can
simply add the two probabilities we have calculated to get:
p(assets nationalized) = 0.48 + 0.12 = 0.60
Probability distributions
So far in this chapter we have looked at how to calculate the probability
that a particular event will occur. However, when we are faced with a
0.60