Question

which of the following values cannot be probabilities?
1, √2, 5/3, 0, −0.6, 0.04, 3/5, 1.16

select all the values that cannot be probabilities.

a. −0.6
b. 1
c. √2
d. 5/3
e. 3/5
f. 0.04
g. 0
h. 1.16

Explanation:

Step1: Recall probability range

Probability values must satisfy \(0 \leq P \leq 1\).

Step2: Analyze each option

• Option A (-0.6): Negative, so \( -0.6 < 0 \), cannot be probability.
• Option B (1): \( 0 \leq 1 \leq 1 \), valid.
• Option C (\(\sqrt{2}\)): \(\sqrt{2} \approx 1.414 > 1\), cannot be probability.
• Option D (\(\frac{5}{3}\)): \(\frac{5}{3} \approx 1.667 > 1\), cannot be probability.
• Option E (\(\frac{3}{5}\)): \(\frac{3}{5} = 0.6\), \(0 \leq 0.6 \leq 1\), valid.
• Option F (0.04): \(0 \leq 0.04 \leq 1\), valid.
• Option G (0): \(0 \leq 0 \leq 1\), valid.
• Option H (1.16): \(1.16 > 1\), cannot be probability.

Answer:

A. \(-0.6\), C. \(\sqrt{2}\), D. \(\frac{5}{3}\), H. \(1.16\)