Question 1203674
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Let P(A) = 0.4 and P(A u B) = 0.6:
(a) For what value of P(B) are A and B mutually exclusive?
(b) For what value of P(B) are A and B independent?
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<pre>
          <U>Part (a) solution</U>


Events A and B are mutually exclusive if and only if  P(A U B) = P(A) + P(B).

In our case, it should be

         0.6 = 0.4 + P(B),

which gives  P(B) = 0.6 - 0.4 = 0.2.


<U>ANSWER</U>.  P(B) = 0.2.


          <U>Part (b) solution</U>


We have a general formula P(A U B) = P(A) + P(B) - P(A n B), which is valid for all events A and B.

If A and B are independent, then  P(A n B) = P(A)*P(B).

So, in our case should be

    0.6 = 0.4 + P(B) - 0.4*P(B),

which implies

    0.6 - 0.4 = 0.6*P(B)

       0.2    = 0.6*P(B)

       P(B) = {{{0.2/0.6}}} = {{{1/3}}}.


<U>ANSWER</U>.  P(B) should be {{{1/3}}}.
</pre>

Solved.