Question

Question 4
Which of the following cannot be the probability of an event?
(a)1/4
(b) 0.6
(c) 5 %
(d)20/19​

Answer 1

Given:

Four options for probability of an event.

(a)1/4

(b) 0.6

(c) 5 %

(d)20/19​

To find:

Which option is not possible as the probability of an event?

Solution:

First of all, let us learn about the probability of an event:

Formula for probability of an event E is as follows:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

Number of favorable cases are chosen from the Total number of cases only.

That means, Number of favorable cases will be lesser than or equal to the total number of cases.

So, their ratio which is represented as the above formula will always be lesser than or equal to 1 and can not be greater than 1.

$\therefore$ Probability of an event E, P(E) can never be greater than 1.

It always lies in the range [0,1]

$0\le P(E)\le 1$

Now, let us consider the given options:

a) $\frac{1}{4}$ = 0.25 which is in the range [0,1]. So, this is valid probability.

b) 0.6 which is in the range [0,1]. So, this is valid probability.

c) $5\% = \frac{5}{100}$ = 0.05 which is in the range [0,1]. So, this is valid probability.

d) $\frac{20}{19} =1.052$ > 1 so not in the range [0,1].

Hence, option d) is the answer.

Probability of an event can not be $\frac{20}{19}$.