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  • Events A and B are such that P (A) = 1/ 2 , P(B) = 7/12 and P (not A or not B) = 1/ 4. State whether A and B are independent?

Q.10    Events A and B are such that P(A)=\frac{1}{2},P(B)=\frac{7}{12}  and P(not \; A \; or\; not\; B)=\frac{1}{4}.  State whether A and B are independent ?

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 If A  and B are two events such that P(A)=\frac{1}{2},P(B)=\frac{7}{12} and P(not \; A \; or\; not\; B)=\frac{1}{4}.  

                    P(A'\cup B')=\frac{1}{4}

                   P(A\cap B)'=\frac{1}{4}                       (A'\cup B'=(A\cap B)')

                   \Rightarrow \, \, 1-P(A\cap B)=\frac{1}{4}

                 \Rightarrow \, \, \, P(A\cap B)=1-\frac{1}{4}=\frac{3}{4}

  Also \, \, \, P(A\cap B)=P(A).P(B)                                       

                P(A\cap B)=\frac{1}{2}\times \frac{7}{12}=\frac{7}{24}       

 As we can see \frac{3}{4}\neq \frac{7}{24}

Hence, A and B are not independent.                                                                           

Posted by

seema garhwal

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