Question

Suppose the probability that the probability of an incumbent president’s re-election given a strong economy is 0.8, and the probability of their re-election given a weak economy is 0.3. If the probability of a strong economy is 0.2, what is the probability of the incumbent’s re-election?

Answer 1

The probability of an incumbent president's re-election given a strong economy is 0.8, and the probability of re-election given a weak economy is 0.3.

The probability of a strong economy is 0.2; this means that the probability of an weak economy is 1-0.2, ie. 0.8.

We have to find the probability of a president's re-election.

Now, by Total probability Theorem, we can say that

=P(Strong Economy)*P(Re-election|Strong Economy)+P(Weak economy)*P(Re-election|Weak Economy)

=(0.2*0.8)+(0.8*0.3)

=0.16+0.24

=0.4

So, the probability of the president's re-election is 0.4.