homework 4 - probability intro: problem 4 (2 points) results for this submission the answer is not correct…
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
Answer
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%)