Question

The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is a divisor of 1". Let B be the event "the outcome is a divisor of 2". Find P(AB). Outcome Probability 1 0.3 2 0.3 3 0.4

Answer 1

We have the following events:

$\begin{gathered} A=\mleft\lbrace outcome\text{ is a divisor of 1}\mright\rbrace\text{ = }\mleft\lbrace1\mright\rbrace \\ B=\mleft\lbrace\text{outcome is a divisor of 2}\mright\rbrace\text{ = }\mleft\lbrace1,2\mright\rbrace \\ A\cap B=\mleft\lbrace1\mright\rbrace \end{gathered}$

then, their probabilities are:

$\begin{gathered} P(A)=P(1)=0.3 \\ P(B)=P(1)+P(2)=0.3+0.3=0.6 \\ P(A\cap B)=P(1)=0.3 \end{gathered}$

then, the probability of A given that B has occurred is the following:

$P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{0.3}{0.6}=0.5$

therefore, P(A|B) = 0.5