If the probability that an event will happen is 0.2, what is the probability of the event's complement?

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Answer 1 · 2018-01-14T11:42:42

$P(A') = 0.8$

If we represent the possibility of the event happening by $A$ then we are given that:

$P(A) = 0.2$

The complement of this is the probability of the event not happening, which we denote by:

$P(barA)$ , or $P(A')$

There are only two possibilities (the event happens or the event doesn't happen) which lead directly t the complement rule:

$P(A) + P(A') = 1$

Hence:

$P(A') = 1 - P(A) =1 - 0.2 = 0.8$