Question

If an event cannot occur then its probability of occurring is:
(a). 1
(b). $\dfrac{2}{3}$
(c). $\dfrac{1}{3}$
(d). 0

Answer 1

Hint: First we will look at the meaning of event and probability and what it implies. Then with the help of definition of event we will find the probability of an event occurring given that it can’t occur.

Complete step-by-step answer:

Let’s first write the definition of some important terms.
Probability: A number expressing the likelihood of the occurrence of a given event, especially a fraction expressing how many times the event will happen in a given number of tests or experiments.
Now we will write the definition of event.
Event: In probability, the set of outcomes from an experiment is known as an Event. So say for example you conduct an experiment by tossing a coin. The outcome of this experiment is the coin landing ‘heads’ or ‘tails’. These can be said to be the events connected with the experiment. So when the coin lands tails, an event can be said to have occurred.
Now if an event cannot occur then the number of outcomes is 0 for that event.
The probability will be,
$P=\dfrac{number\text{ of outcomes of that event}}{total\text{ number of outcomes}}$
Now the number of outcomes of this event is 0.
Substituting its value in $P=\dfrac{number\text{ of outcomes of that event}}{total\text{ number of outcomes}}$ we get,
$P=\dfrac{0}{total\text{ number of outcomes}}=0$
Hence, the answer is option (d).

Note: In this question students might get confused that the total number of outcomes is not given, but as the number of outcomes of the given event is 0 so, we don’t need the total number of outcomes value. The total probability of an event is 1, i.e the probability of an event occuring + the probability of an event not occurring = 1. So, we cannot choose option (a), it will be wrong.