Question

In: Statistics and Probability

If P(A)=0.8, P(B)=0.5, and P(C)=0.4, find P(A ∩ (Bc ∪ Cc )) if A, B, and...

If P(A)=0.8, P(B)=0.5, and P(C)=0.4, find P(A ∩ (B^c ∪ C^c )) if A, B, and C are independent.

Expert Solution

Solution:

Given:

P(A) = 0.8 , P(B) = 0.5 , P(C)= 0.4 , Events A , B and C are independent.

We have to find:

Since A , B and C are independent events, we can write :

By using De'Morgans Law,

Thus

By complement rule of Probability :

P(A^c) = 1 - P(A) ,

then

Thus we get:

Since events are independent

Now substituting given probabilities , we get:

orchestra answered 2 years ago

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