Question

which of the following values cannot be probabilities? 0.03, - 0.42, 1, 3/5, 0, 1.23, 5/3, √2 select all the values that cannot be probabilities. a. 5/3 b. 0 c. -0.42 d. 1 e. 0.03 f. 3/5 g. √2 h. 1.23

Explanation:

Step1: Recall probability range

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

Step2: Analyze option A

\(\frac{5}{3}\approx1.67> 1\), so it cannot be a probability.

Step3: Analyze option B

\(0\) is a valid probability (for an impossible event).

Step4: Analyze option C

\(- 0.42<0\), so it cannot be a probability.

Step5: Analyze option D

\(1\) is a valid probability (for a certain event).

Step6: Analyze option E

\(0.03\) is between \(0\) and \(1\), so it is a valid probability.

Step7: Analyze option F

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

Step8: Analyze option G

\(\sqrt{2}\approx1.414>1\), so it cannot be a probability.

Step9: Analyze option H

\(1.23>1\), so it cannot be a probability.

Answer:

A. \(\frac{5}{3}\), C. \(-0.42\), G. \(\sqrt{2}\), H. \(1.23\)