Question 1195432
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Suppose events A, B, and C are independent and
P(A) = 1/4, P(B) = 1/5, P(C) = 1/8
Find the probability. (Enter the probability as a fraction.)
P[(A ∪ B) ∩ C]
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<pre>
P(A U B) = P(A) + P(B) - P(A &#8745; B) = {{{1/4)}}} + {{{1/5}}} - {{{(1/4)*(1/5)}}} = {{{5/20 + 4/20 - 1/20}}} = {{{8/20}}} = {{{2/5}}}.


Next, since A, B and C are independent events, the events (A U B) and C are independent events, too.


Therefore,  P((A U B) &#8745; C) = P(A U B) * P(C) = {{{(2/5)*(1/8)}}} = {{{1/20}}}.    <U>ANSWER</U>
</pre>

Solved.