Question

which of the following values cannot be probabilities?
1,5/3,0,3/5, - 0.47,1.34,\sqrt{2},0.08
select all the values that cannot be probabilities.
□ a. 0.08
□ b. 1
□ c. \sqrt{2}
□ d. 1.34
□ e. - 0.47
□ f. 0
□ g. 5/3
□ h. 3/5

Explanation:

Step1: Recall the probability range

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

Step2: Check each value

• For \(0.08\):

Since \(0 < 0.08<1\), it can be a probability.

• For \(1\):

Since \(0\leq1\leq1\), it can be a probability (certain event).

• For \(\sqrt{2}\approx1.414\):

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

• For \(1.34\):

Since \(1.34>1\), it cannot be a probability.

• For \(- 0.47\):

Since \(-0.47 < 0\), it cannot be a probability.

• For \(0\):

Since \(0\leq0\leq1\), it can be a probability (impossible event).

• For \(\frac{5}{3}\approx1.667\):

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

• For \(\frac{3}{5} = 0.6\):

Since \(0<\frac{3}{5}<1\), it can be a probability.

Answer:

C. \(\sqrt{2}\), D. \(1.34\), E. \(-0.47\), G. \(\frac{5}{3}\)