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The probability of event A occurring is 0.5 and of B occurring is 0.3. If A and B are mutually exclusive events then the probability of neither A nor B occurring is___

Solution : 0.2
P(A' UNION B' ) = 1- P(A UNION B)
                            1-0.8

                            = 0.2



My Solution :   1

P(A' UNION B' ) = P ( A INTERSECTION B )'       using demorgans law
                           = 1- P ( A INTERSECTION B )

                            = 1 - 0 ( mutually exclusive )

                            =1
 

Which is the correct approach . Please Help

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"neither A nor B" means "A doesn't occur AND B also doesn't occur".
ie P(A' INTERSECTION  B')
=P(A UNION B)'
=1- P(A UNION B)
=1-(P(A)+P(B))
= 1-0.8 =0.2

What you have taken "P(A' UNION B' )" is "A doesn't occur OR B doesn't occur".

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