Question

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

Explanation:

Step1: Recall the probability range

The probability \(P(E)\) of an event \(E\) satisfies \(0\leq P(E)\leq1\) (or \(0\%\leq P(E)\leq100\%\)).

Step2: Analyze each option

• Option A: \(333.3\%=\frac{333.3}{100} = 3.333>1\). Probability values cannot be greater than \(100\%\) (or \(1\)), so A is incorrect.
• Option B: \(- 0.0009<0\). Probability values cannot be negative, so B is incorrect.
• Option C: \(0\) satisfies \(0\leq P(E)\leq1\). A probability of \(0\) means the event is impossible, so C is correct.
• Option D: \(\frac{120}{101}\approx1.188>1\). Probability values cannot be greater than \(1\), so D is incorrect.
• Option E: \(2.3 > 1\). Probability values cannot be greater than \(1\) (not \(100\) as the unit - less probability is in the range \([0,1]\)), so E is incorrect.
• Option F: \(\frac{15}{15}=1\). A probability of \(1\) means the event is certain, so F is correct.

Answer:

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