**19. Incorrect. The answer is false not true.** In order to
calculate the probability that well A_{2} contained commercial
reserves, we have to employ the Bayes's rule. The
essence of the Bayesian approach is to provide a mathematical rule explaining how
you should change your existing beliefs in the light of new evidence. In other
words, it allows statistician to combine new data with their existing knowledge
or expertise.

In the context of the wildcat exploration, we
can think about Bayes' rule in terms of updating the
belief that well A_{2} contains commercial reserves in the light of the
confirmation of the existence of profitable reserves (event B). Specifically,
our posterior belief P(A|B) is calculated by multiplying our prior belief P(A)
by the likelihood P(B|A) that B will occur if A is true:

The power of Bayes'
rule is that in many situations where we want to compute P(A|B)
it turns out that it is difficult to do so directly, yet we might have direct
information about P(B|A). Bayes' rule enables us to
compute P(A|B) using P(B|A).

Applying the Bayes' rule, we can calculate the
probability that profitable reserves come from well A_{2}:

_{ }

P(A_{2} | B) = (0.25*0.3) / 0.19 = 39.47%