Question

QuestionSuppose A and B are dependent events. If P(A) = 05 and P(BIA) = 0.6, what isP(AB)?

Answer 1

We have to calculate P(A∩B), knowing that P(A) = 0.5 and P(B|A) = 0.6.

We can relate this probabilities as:

`\begin{gathered} P(A\cap B)=P(B|A)\cdot P(A) \\ P(A\cap B)=0.6\cdot0.5 \\ P(A\cap B)=0.3 \end{gathered}`

This can be thinked as:

The probability of both events, A and B (represented by the intersection of A and B), is equal to the probability of event A times the probability of event B, given that event A has happened.

Answer: P(A∩B) = 0.3