Question

which of the following values cannot be probabilities?
3/5, 5/3, -0.44, 1, 0, 1.37, √2, 0.02
select all the values that cannot be probabilities.
a. 5/3
b. 1.37
c. -0.44
d. 0
e. 3/5
f. √2
g. 1
h. 0.02

Explanation:

To determine which values cannot be probabilities, we use the definition of a probability: a probability must be a number between 0 and 1 (inclusive).

Step 1: Analyze each option

• Option A: \( \frac{5}{3} \)

\( \frac{5}{3} \approx 1.67 \), which is greater than 1. Probabilities cannot exceed 1, so this cannot be a probability.

• Option B: \( 1.37 \)

1.37 is greater than 1. Probabilities must be \( \leq 1 \), so this cannot be a probability.

• Option C: \( -0.44 \)

Probabilities cannot be negative (they represent the likelihood of an event, which is non - negative). So this cannot be a probability.

• Option D: \( 0 \)

0 is a valid probability (it represents an impossible event).

• Option E: \( \frac{3}{5} \)

\( \frac{3}{5}=0.6 \), which is between 0 and 1. So this is a valid probability.

• Option F: \( \sqrt{2} \)

\( \sqrt{2}\approx1.414 \), which is greater than 1. So this cannot be a probability.

• Option G: \( 1 \)

1 is a valid probability (it represents a certain event).

• Option H: \( 0.02 \)

0.02 is between 0 and 1. So this is a valid probability.

Answer:

A. \( \frac{5}{3} \), B. \( 1.37 \), C. \( -0.44 \), F. \( \sqrt{2} \)