Question

homework 4 - probability intro: problem 4 (2 points) results for this submission the answer is not correct. which of the following numbers can be probabilities? (select all that apply) a. 4/10 b. 100% c. 0.1 d. 101/200 e. 0.02% f. 99% g. 0 h. 1 i. -31/89 j. 6/6 k. -3.5 l. 1/2 m. 101/50 n. 72 o. 17/53 p. 150% q. 0.68/2 r. 1.48 s. 25% t. 12

Explanation:

Step1: Recall probability range

A probability \(P\) satisfies \(0\leq P\leq1\). We will check each option against this range.

Step2: Check option A

\(\frac{4}{10}=0.4\), and \(0\leq0.4\leq1\), so it can be a probability.

Step3: Check option B

\(100\% = 1\), and \(0\leq1\leq1\), so it can be a probability.

Step4: Check option C

\(0.1\) satisfies \(0\leq0.1\leq1\), so it can be a probability.

Step5: Check option D

\(\frac{101}{200}=0.505\), and \(0\leq0.505\leq1\), so it can be a probability.

Step6: Check option E

\(0.02\%=\frac{0.02}{100}=0.0002\), and \(0\leq0.0002\leq1\), so it can be a probability.

Step7: Check option F

\(99\% = 0.99\), and \(0\leq0.99\leq1\), so it can be a probability.

Step8: Check option G

\(0\) is within the range \(0\leq P\leq1\), so it can be a probability.

Step9: Check option H

\(1\) is within the range \(0\leq P\leq1\), so it can be a probability.

Step10: Check option I

\(-\frac{31}{89}<0\), so it cannot be a probability.

Step11: Check option J

\(\frac{6}{6}=1\), and \(0\leq1\leq1\), so it can be a probability.

Step12: Check option K

\(- 3.5<0\), so it cannot be a probability.

Step13: Check option L

\(\frac{1}{2}=0.5\), and \(0\leq0.5\leq1\), so it can be a probability.

Step14: Check option M

\(\frac{101}{50}=2.02>1\), so it cannot be a probability.

Step15: Check option N

\(72>1\), so it cannot be a probability.

Step16: Check option O

\(\frac{17}{53}\approx0.321\), and \(0\leq0.321\leq1\), so it can be a probability.

Step17: Check option P

\(150\%=\frac{150}{100}=1.5>1\), so it cannot be a probability.

Step18: Check option Q

\(\frac{0.68}{2}=0.34\), and \(0\leq0.34\leq1\), so it can be a probability.

Step19: Check option R

\(1.48>1\), so it cannot be a probability.

Step20: Check option S

\(25\% = 0.25\), and \(0\leq0.25\leq1\), so it can be a probability.

Step21: Check option T

\(12>1\), so it cannot be a probability.

Answer:

A. \(\frac{4}{10}\), B. \(100\%\), C. \(0.1\), D. \(\frac{101}{200}\), E. \(0.02\%\), F. \(99\%\), G. \(0\), H. \(1\), J. \(\frac{6}{6}\), L. \(\frac{1}{2}\), O. \(\frac{17}{53}\), Q. \(\frac{0.68}{2}\), S. \(25\%\)