Question

Determine which number could not be used to represent the probability of the event.

Select all that apply.

• A. $-1.5$, because probability values cannot be less than $0$.
• B. $0.0002$, because probability values must be rounded to two decimal places.
• C. $\frac{64}{25}$, because probability values cannot be greater than $1$.
• D. $33.3\%$, this is because probability values cannot be greater than $1$.
• E. $\frac{320}{1058}$, because probability values cannot be in fraction form.

Answer 1

Answer: (A), (C)

$\frac{64}{25}$, because probability values cannot be greater than $1$.

Step-1: Explanation for the correct options:

We know that probability $P\left(E\right)$ of any event $E$, $0\le P\left(E\right)\le 1$,

In option $A$, given $P\left(E\right)=-1.5$ which is wrong, so we cannot represent probability by $-1.5$.

In option $C$, given $P\left(E\right)=\frac{64}{25}$ and $\frac{64}{25}=2.56>1$, which is wrong, so we cannot represent probability by $\frac{64}{25}$.

Therefore, option $A$ and $C$ are wrong representation of probability.

Step-2: Explanation for the incorrect options:

In option $B$, given $P\left(E\right)=0.0002$ and $0\le 0.0002\le 1$, which is correct representation of probability.

In option $D$, given $P\left(E\right)=33.3\%$ and $33.3\%=\frac{33.3}{100}=0.333<1$, which is correct way to represent probability.

In option $E$, given $P\left(E\right)=\frac{320}{1058}$, since the probability of number can be represented in fraction form if numerator of positive fraction is less than denominator, hence this is also correct representation of probability.

Hence, correct options are $A$ and $C$.