Question

Please helpwhat does A∩B=∅ mean. Thus, please help with:Suppose Pr(A)=0.3, Pr(B)=0.4 and A∩B=∅. Find:a- Pr(A∩B)b- Pr(A∪B)

Answer 1

Given: A and B are two sets such that-

`\begin{gathered} A\cap B=\phi \\ Pr(A)=0.3 \\ Pr(B)=0.4 \end{gathered}`

Required: To determine-

`\begin{gathered} Pr(A\cap B) \\ Pr(A\cup B) \end{gathered}`

Explanation: Since A and B have no common elements, the events are independent events or disjoints or mutually exclusive.

For independent events, we have-

`Pr(A\cap B)=Pr(A).Pr(B)`

Substituting the values into the formula-

`\begin{gathered} Pr(A\cap B)=0.3*0.4 \\ =0.12 \end{gathered}`

Recall that-

`Pr(A\cup B)=Pr(A)+Pr(B)-Pr(A\cap B)`

Substituting the values into the formula and further solving as-

`\begin{gathered} Pr(A\cup B)=0.3+0.4-0.12 \\ =0.7-0.12 \\ =0.58 \end{gathered}`

Final Answer: a)

`Pr(A\cap B)=0.12`

b)

`Pr(A\cup B)=0.58`