Question

multiple choice: which of the following numbers could not represent a probability? write a sentence explaining why they could not. (a) $-\frac{1}{10}$ (b) 1 (c) 1% (d) 0.1

Explanation:

Step1: Recall probability range

The probability $P$ of an event satisfies $0\leq P\leq1$.

Step2: Analyze option A

$-\frac{1}{10}=- 0.1<0$, so it cannot be a probability.

Step3: Analyze option B

$1$ is within the range $0\leq P\leq1$, so it can be a probability.

Step4: Analyze option C

$1\%=\frac{1}{100}=0.01$, and $0\leq0.01\leq1$, so it can be a probability.

Step5: Analyze option D

$0.1$ is within the range $0\leq0.1\leq1$, so it can be a probability.

Answer:

A. $-\frac{1}{10}$ because probability values must be between 0 and 1 (inclusive), and $-\frac{1}{10}<0$.