Question

The probability of a certain event is
(a) 0
(b) 1
(c) greater than 1
(d) less than 0

Answer 1

Hint:
Here, we need to find the probability of a certain event. We will use the definition and formula for probability of an event, with some examples to check the given options and find the probability of a certain event. A certain event is an event which is sure to happen.

Complete step by step solution:
A certain event is an event which is sure to happen.
The probability of an event is the chance of that event occurring.
For example: The probability of picking 5 red balls out of a bag having 6 red balls, 7 green balls, and 10 blue balls is the chance of selecting 5 red balls out of the bag.
The probability of an event is given by \[P\left( E \right) = \dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Number of total outcomes}}}}\].
We will check each of the given options using the definition of probability and its formula.
The probability of an event is 0 if the number of favourable outcomes is 0.
This means that there is no chance that the event can take place.
For example: The probability of picking 5 white balls out of a bag having 6 red balls, 7 green balls, and 10 blue balls is 0.
Therefore, the probability of a certain event cannot be 0.
Thus, option (a) is incorrect.
The probability of an event is 0 if the number of favourable outcomes is equal to the number of total outcomes.
This means that there is 100 percent chance that the event will take place.
For example: If a biased coin has heads on both sides, then every toss will result in a heads. Thus, the probability that a heads will come when the biased coin is tossed is 1.
We can say that the event of getting heads on such a biased coin is a certain event.
Therefore, the probability of a certain event is 1.

Thus, option (b) is correct.

Note:
We will also check the other options.
The number of favourable outcomes can never be greater than the number of total outcomes.
For example: It is not possible to pick 15 balls from a bag having only 6 balls.
Thus, the probability of an event can never be greater than 1. Option (c) is incorrect.
Also, the number of favourable outcomes is always a whole number.
Therefore, the number of favourable outcomes cannot be negative.
Thus, the probability of an event cannot be negative. Option (d) is incorrect.
We can conclude that the probability of an event always lies between 0 and 1, both inclusive.