Question

Which of the following is a correct statement about probability?
A) It must have a value between −1 and 1.
B) It is the collection of multiple experiments.
C) The result can be in the form of decimal or negative.
D) The probability of an event will not be less than 0.

Answer 1

In this question, four options are given and we have to choose which statement is correct. Probability always lies between 0 and 1 i.e. $0 \leqslant P \leqslant 1$.

Complete step by step solution: First of all, let us discuss what is probability. Probability means chances of an event to occur or what is the possibility that a certain thing will happen.
For example, I have to buy medicine and I will make a guess that the shop will open or not at night. The shop usually closes early on Sunday and the chances of the opening of the shop are $20\%$. So, the chances of the opening of the shop are less.
If the event to happen is called favourable outcomes and total events are known as total outcomes. Then, the formula for probability is given as follow:

$\Rightarrow \text{Probability} = \dfrac{\text{Favourable Outcomes}}{\text{Total Outcomes}}$

If an event can’t be possible than the event is called an impossible event. E.g. what is the possibility of coming 7 while rolling a die. Die has only 6 phases i.e. 1, 2, 3, 4, 5 and 6 number and hence 7 will not come on die. So, it is called an impossible event. Probability of 7 number is 0

$\Rightarrow \operatorname{P} (7) = 0$

If an event is certain that it will happen for sure than it is known as a certain event. E.g. coming of number 1 to 6 on rolling a die. The die has 6 numbers and anyone number can come hence it is a certain event and probability is 1.

$\Rightarrow \operatorname{P} (1 to 6) = 1$

You can see the probability can be 0 or 1. It can be any value between 0 and 1. Minimum probability is zero and the maximum is 1. But it will never be less than 0.
So, options A and C can never be correct. As in first the statement option is $- 1 \leqslant P \leqslant 1$, it includes negative value which is not true.
In C they say that probability can be in form of decimal or negative. Probability can be any decimal between 0 and 1 but never negative. Hence, this option is wrong.
In option B, they say that probability is the collection of multiple experiments. It is wrong, as the probability is the collection of different outcomes of one experiment.
Option D is the correct because in this statement they say that I can never less than 0 which is true

So, D is the correct option.

Note: Probability plays an important part in the weather prediction, data analysis, in daily life etc. in probability sample space is the set of possible outcomes during an event. E.g. sample space of rolling a die is $\\{ 1,2,3,4,5,6\\}$. If two events have equal chances to occur than they said to be equally likely events. E.g. while rolling a die getting an odd number and getting an even number, chances in the occurrence of these events are same. So, they are equally likely events.