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)=(P(A\cap B))/(P(B))=(0.3)/(0.6)=0.5`

therefore, P(A|B) = 0.5