Question

please answer this question

If events A and B are independent, such that P( A) = \(\frac { 3 }{ 5 }\), P (B) = \(\frac { 2 }{ 3 }\), find P(A∪B).​

Answer 1

Answer:

Given P(A)=1/2 and P(B)=1/5

we know that for two independent events  A,B. 

⇒ P(A∩B)=P(A)*P(B)

⇒P(A∩B)=1/2∗1/5=1/10

⇒1) P(A∪B)=P(A)+P(B)-P(A∩B)     

                     =1/2+1/5−1/10       

                       =3/5

⇒2) P(A/B)=P(A∩B)/P(B) 

                        =(1/5)(1/10)        

                        =21

3)P(A/A∪B)=P(A∩(A∪B))/P(A∪B)     [ since P(A∩(A∪B))=P(A)]

P(A/A∪B)=P(A)/P(A∪B)

                   =(3/5)(1/2)

                   =65

Explanation:

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