Question

If the probability of happening of an event is p, then the probability of its not happening is:
A) $p - 1$
B) $1 - p$
C) $1 - \dfrac{1}{p}$
D) $p$

Answer 1

According to the question given the probability of an event not to happen if the probability of happening of an event is p. So, first of all we have to probability of an event to be happen,
As we know that for any event it is the sum of the probability of an event to happen and probability of an event not to happen is equal to 1.
Now, we have to rearrange the event as we have obtained from the above statement. So, with the help of the statements we can obtain the probability of it not happening.

Complete step-by-step answer:
Step 1: First of all as we know that for any event it is the sum of the probability of an event to happen and probability of an event not to happen is equal to 1. Hence,
$\Rightarrow$ P(an event to be happen) + P(an event not to be happen) = 1……………………(1)
Step 2: Now, we have to rearrange the expression (1) as obtained in the solution step 1.
$\Rightarrow$P(an event to be happen) = 1 - P(an event not to be happen)…………………….(2)
Step 3: Now, on again rearranging the terms of the expression (2) as obtained in the solution step 2,
$\Rightarrow$P(an event not to be happen) = 1 - P(an event to be happen)
Hence, we have obtained the probability of it not happening is: $1 - p$.

Therefore the correct option is (B).

Note: If the probability of an event to occur is p then the probability of an event not to occur can be obtained by subtracting the probability of an event to occur by one. Probability of an event will always be in between 0 to 1.