Question

The probability of the complement of an event is ____ less than the probability of the event itself.

A. Not enough information provided to answer the question.
B. Sometimes
C. Always
D. Never

Answer 1

Choice B) Sometimes

Answer 2

Answer: Choice B) Sometimes

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Step-by-step explanation:

Consider two events A and B. Let's make these two events complementary. This means that either one or the other happens, but not both at the same time. By this definition, this means

P(A) + P(B) = 1

Now let's assign a probability to event A. Let's make
P(A) = 0.3

That would mean...
P(A) + P(B) = 1
P(B) = 1 - P(A)
P(B) = 1 - 0.3
P(B) = 0.7

So event B is more likely. If event A is the original event, then event B as the complementary event has a higher probability.

So this initially implies that the answer would be "Always"; however, we can easily flip things around. Let's say that
P(A) = 0.7

That would lead to P(B) = 0.3. All I've done here is swap the roles of events A and B. Now event A is more likely with a higher probability.

So this means that the answer is "Sometimes". It depends on if the initial event's probability. If the initial event has a probability less than 0.5, then the answer is "yes the complementary event is more likely". If the initial event's probability is greater than 0.5 then the answer is "no, the complementary event is not more likely"