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
`(3)/(5),2,0,1,-0.45, 1.44`.

To find:

All the values that cannot be probabilities.

Solution:

We know that,

`\text{Probability}=\frac{\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
`(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`.