Question

which of the following values cannot be probabilities? 3/5, -0.52, 1, 0, 1.37, 5/3, 0.04, √2 select all the values that cannot be probabilities. a. 3/5 b. 1.37 c. 5/3 d. 0.04 e. 0 f. -0.52 g. 1 h. √2

Explanation:

Step1: Recall probability range

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

Step2: Analyze each value

• \(\frac{3}{5}=0.6\), and \(0\leq0.6\leq1\), so it can be a probability.
• \(1.37> 1\), so it cannot be a probability.
• \(\frac{5}{3}\approx1.67>1\), so it cannot be a probability.
• \(0.04\), and \(0\leq0.04\leq1\), so it can be a probability.
• \(0\) is a valid probability (impossible - event).
• \(- 0.52<0\), so it cannot be a probability.
• \(1\) is a valid probability (certain - event).
• \(\sqrt{2}\approx1.414>1\), so it cannot be a probability.

Answer:

B. 1.37, C. \(\frac{5}{3}\), F. - 0.52, H. \(\sqrt{2}\)