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The term "probability" simply refers to the likelihood of something occurring. We can talk about the probabilities of certain outcomes鈥攈ow likely they are鈥攚hen we're unsure about the outcome of an event. Statistics is the study of occurrences guided by probability.

In the exercise, we are given that

\(\begin{array}{l}P(A) &=& 0.6\\P(B) &=& 0.05\\B \subseteq A\end{array}\)

From \(B \subseteq A\)

we have

\(A \cap B = B \Rightarrow P(A \cap B) = P(B) = 0.05\)

Conditional probability of A given that the event B has occurred, for which \(P(B) > 0\),\(P(A\mid B) = \frac{{P(A \cap B)}}{{P(B)}}\)\(\)

for any two events A and B.

From the definition we have

\(P(B\mid A) = \frac{{P(B \cap A)}}{{P(A)}} = \frac{{P(B)}}{{P(A)}} = \frac{{0.05}}{{0.6}} = 0.0833\)