Question

determine which numbers could be used to represent the probability of an event. select all that apply. a. 0, because probability values can equal 0. b. 2.3, because probability values cannot be greater than 100. c. $\frac{15}{15}$, because probability values can equal 1. d. 333.3%, because probability values can be greater than 100%. e. - 0.0009, because probability values must be between - 1 and 1. f. $\frac{120}{101}$, because probability values cannot be greater than 1.

Explanation:

Step1: Recall probability range

The probability of an event \(P(E)\) satisfies \(0\leq P(E)\leq1\).

Step2: Analyze option A

\(0\) is within the range \(0\leq P(E)\leq1\), so it can represent a probability.

Step3: Analyze option B

\(2.3> 1\), so it cannot represent a probability.

Step4: Analyze option C

\(\frac{15}{15}=1\), and since \(1\) is within the range \(0\leq P(E)\leq1\), it can represent a probability.

Step5: Analyze option D

\(333.3\%=\frac{333.3}{100}=3.333>1\), so it cannot represent a probability.

Step6: Analyze option E

\(- 0.0009<0\), so it cannot represent a probability.

Step7: Analyze option F

\(\frac{120}{101}\approx1.188 > 1\), so it cannot represent a probability.

Answer:

A. 0, because probability values can equal 0.
C. \(\frac{15}{15}\), because probability values can equal 1.