Question

The probability of E that is P (E) = 0.05. Then find the probability of not E?

Answer 1

Hint: The probability of E is given to be 0.05. Now we know that probability of not E is given by (1 – probability of E) that is (1 – P (E)). Hence we will use this formula to find the required probability.

Complete step by step answer:
Now we are given that probability of E is 0.05
That is P (E) = 0.05.
Now this means the probability that event E happens is 0.05.
Now we know that the sum of all the probabilities of all possible mutually exclusive events of an experiment is 1.
Now we have that event E either happens or not happens.
Also these two are mutually exclusive events. Since it can’t be that the event happens and not happens at the same time.
Hence we can say that the probability of E + the probability of not E = 1
That is P (E) + P (Not E) = 1.
Now let us check this by a known example.
Let the experiment be tossed.
Let A be the event that we get heads.
Now we know that P (A) = 0.5.
Now if we don’t get heads then the result is tails.
Now calculate the probability of not A.
Probability of not A = 1 – 0.5 = 0.95.
As we know probability of not A means probability of tails which is indeed 0.95.

Hence we say that the probability of not E is = 0.95.

Note: Note that the result of the sum of mutually exclusive probabilities is one if all the cases are considered, that is all mutually exclusive possible events. For example if a coin is tossed then there are 2 mutually exclusive events, getting a head and tail. Hence probability of getting a head + probability of getting a tail is 1.