11.give that : P(A)=P(B)=P(C)=1/4,P(A∩B)=P(C∩B)=0 and P(A∩C)=1/8 ,compute the probability that at least one of the three events A,B or C will occur .
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12 . suppose that :P(A)=0.4 , P(B)=α ,P(AUB)= 0.7:
i.what is the value of α which makes A and B disjoint ?
ii. what is the value of αwhich makes A and B independent ?
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13 . show that:
i. P(A∩B∩C)=P(A|B∩C)P(B|C)P(C)
Hello, compufatwa!
Here's #12 . . .
We have: .12 . Given: .
a) What is the value of which makes A and B disjoint?
Hence: . .[1]
If A and B are disjoint, then
Then [1] becomes: .
b) What is the value of which makes A and B independent ?
If A and B are independent, then: .
Then [1] becomes: .
Therefore: .