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

5 answers
Question:

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

Answers

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

The probability of the complement of an event is (SOMETIMES) less than the probability of the event itself.

B. Never
The event has to happen in order to be complemented. Not every event is complemented, but the event itself can only and always be an event.

Choice B) Sometimes




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"

The probability of the complement of an event is d) sometimes less than the probably of the event itself.

Your complement c=1-p
If you think of a dice you could have the probability to "get the number 1" =1/6, so its complement would be 5/6 which is clearly more
if your event is instead "get a number from 1 to 6" then your probability would be 1=100% and the complement 0 which is less.

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