Question

which of the following values cannot be probabilities?
1, 5/3, 3/5, 1.3, 0, -0.45, √2, 0.06

select all the values that cannot be probabilities.
□ a. ( \frac{5}{3} )
□ b. 0.06
□ c. 1
□ d. ( \frac{3}{5} )
□ e. ( sqrt{2} )
□ f. 0
□ g. -0.45
□ h. 1.3

Explanation:

Step1: Recall probability range

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

Step2: Analyze each option

• Option A (\( \frac{5}{3} \)): \( \frac{5}{3} \approx 1.67 > 1 \), so it can't be a probability.
• Option B (0.06): \( 0 \leq 0.06 \leq 1 \), so it can be a probability.
• Option C (1): \( 0 \leq 1 \leq 1 \), so it can be a probability.
• Option D (\( \frac{3}{5} \)): \( \frac{3}{5} = 0.6 \), \( 0 \leq 0.6 \leq 1 \), so it can be a probability.
• Option E (\( \sqrt{2} \)): \( \sqrt{2} \approx 1.414 > 1 \), so it can't be a probability.
• Option F (0): \( 0 \leq 0 \leq 1 \), so it can be a probability.
• Option G (-0.45): \( -0.45 < 0 \), so it can't be a probability.
• Option H (1.3): \( 1.3 > 1 \), so it can't be a probability.

Answer:

A. \( \frac{5}{3} \), E. \( \sqrt{2} \), G. \( -0.45 \), H. \( 1.3 \)