Question

In which event, the experiment is impossible?
A. Tossing a coin for head or tail.
B. 5 in case of throwing a dice.
C. Rolling a dice for 7.
D. Tossing a coin to get a tail.

Answer 1

Hint- In this question, first we will see the definition of probability. Next we will see the definition of impossible events with some examples. We will use the formula of probability to find the probability of impossible events. Then we check options for impossible events.

Complete step by step solution:
Probability of an event indicates how likely an event can occur. Mathematically, we can write:
$P(E) = \dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Total possible outcomes}}}}$ . (1)
Let us define events in probability.
The outcomes of a random experiment are called the events of the experiment.
For example- in tossing a coin, the outcomes head and tail are events of the experiment.
Impossible events:-
An event which cannot occur at any circumstances or at any performance of the experiment is called an impossible event.
So, we can say that for impossible events, the number of outcomes is zero.
Using equation 1, we can write:
$P(E) = \dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Total possible outcomes}}}} = \dfrac{0}{{{\text{Total possible outcomes}}}} = 0$ .
Therefore in other words, an event E is called an impossible event if its probability is zero.
Now on going through the options, on rolling a dice there are six possible outcomes. Sample space for the experiment is given as: \left\\{ {1,2,3,4,5,6} \right\\}. So, the occurrence of 7 on rolling the dice is an impossible event. Therefore, its probability is 0.
So, option C is an example of an impossible event.

Note- This question is based on types of events. So you should know the definition of event in probability and its type. The probability of a random event always lies between 0 and 1. For sure events, the probability is 1.