Question

Which of the following values cannot be​ probabilities? 3/5​, 2​, 0​, 1​, −0.45​, 1.44​, 0.05​, 5/3 Select all the values that cannot be probabilities.

Answer 1

Given:

The numbers are $\dfrac{3}{5},2,0,1,-0.45, 1.44$.

To find:

All the values that cannot be probabilities.

Solution:

We know that,

$\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}$

The minimum value of favorable outcomes is 0 and the maximum value is equal to the total outcomes. So, the value of probability lies between 0 and 1, inclusive. It other words, the probability lies in the interval [0,1].

$0\leq \text{Probability}\leq 1$

From the given values only $\dfrac{3}{5}, 0, 1$ lie in the interval [0,1]. So, these values can be probabilities.

The values $2,-0.45, 1.44$ does not lie in the interval [0,1]. So, these values cannot be probabilities.

Therefore, the correct values are $2,-0.45, 1.44$.