Question

The probability that it will rain today is \[0.84\]. What is the probability that it will not rain today?

Answer 1

Hint: We are given the probability that it will rain and we have to find it so that it will not rain. Since rain and not rain are complementary situations, we need to keep in mind that the sum of probabilities of an event and its complementary event is 1. An event with a probability of 1 can be considered a sure event, an event with a probability of .5 can be considered to have equal odds of occurring or not occurring and an event with a probability of 0 can be considered an impossible event.

Complete step-by-step solution:
Sample Space: The sample space associated with a random experiment is the set of all possible outcomes. An event is a subset of the sample space.
Event: An event E is said to occur on a particular trial of the experiment if the outcome observed is an element of the set E.
The probability formula is defined as the probability of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.
Probability (event) \[ = \dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}\]
The sum of probabilities of an event and its complementary event is \[1\].
We are given that the probability that it will rain today is \[0.84\].
Since the sum of probabilities of all the possible events is \[1\].
Therefore the probability that it will not rain today \[ = 1 - 0.84 = 0.16\]
Hence we get the required answer.

Note: To solve such a question one must be aware of complementary events and relation between their probabilitiesProbability of any event can be between 0 and 1 only. Probability of any event can never be greater than 1. Probability of any event can never be negative.