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Let $A, B$ and $C$ be independent events which occur with probabilities $0.8, 0.5$ and $0.3$ respectively. The probability of occurrence of at least one of the event is _____
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## 2 Answers

+12 votes
Best answer
$P(A) = 0.8$ $\implies$ $P(A') =$ $1 - 0.8 = 0.2$

$P(B) = 0.5$ $\implies$ $P(B')$ = $1 - 0.5 = 0.5$

$P(C) = 0.3$ $\implies$ $P(C')$ = $1 - 0.3 = 0.7$

$P$(No event will occur): =$0.2 * 0.5 * 0.7 = 0.07$

$P$(at least 1 event will occur): $1 - 0.07 = 0 .93$
answered by Boss (40.2k points)
edited
+1 vote
P(at least A or B or C )= P(A u B u c)

= 0.8+0.5+0.3-(0.8*0.5) -(0.5 *0.3) -(0.8*0.3)+(0.8*0.5*0.3)

=1.6-0.67

=0.93
answered by Active (2.6k points)
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