Question & Answer
QUESTION

The probability that it will rain today is 0.76. What is the probability that it will not rain today?
(a). 0.76
(b). 0.24
(c). 0
(d). 1

ANSWER Verified Verified
Hint: We need to use the basic probability formula that the total probability of all the events should be equal to 1.

Complete step-by-step answer:
It is given that the probability that it will rain today is 0.76. However, there can be only two possible options, it will rain today or it will not rain today.
Now, from the theory of probability, we know that
$\text{Total Probability of all possible events=1 }............\text{(1}\text{.1)}$
In this case let P(rain) denote the probability that it will rain today and let P(not rain) denote the probability that it will not rain today. We know that the only possible events are that it will rain and it will not rain. Then, from equation (1.1), we find that
$P(rain)+P(not\text{ }rain)=1\text{ }.............\text{(1}\text{.2)}$
It is given in the question that $P(rain)=0.76$. Thus, using it in equation (1.2), we find
$P(not\text{ }rain)=1-P(rain)=1-0.76=0.24$
Thus, we find that the probability that it will not rain is equal to 0.24 which matches the answer in option (b). Hence option (b) is the correct answer to this question.

Note: In this case, there were only two possible events, however in case that there are more than two possible events, the total sum of the probabilities will always be equal to 1.