Question

an experiment is conducted for which the sample space is ( s={s_1,s_2,s_3,s_4,s_5} ). is the following probability assignment possible for this experiment?

is the probability assignment possible for this experiment?
a. no, because not all of the probabilities are between 0 and 1, inclusive.
b. no, because the probabilities are given as fractions instead of decimals.
c. yes, because both rules for an acceptable probability assignment are satisfied.
d. no, because none of the rules for an acceptable probability assignment are satisfied.
e. no, because the sum of the probabilities of all possible outcomes is not 1.

Explanation:

Step1: Check the range of probabilities

Each probability \(\frac{1}{4}=0.25\), \(\frac{1}{5} = 0.2\), \(\frac{1}{6}\approx0.167\), \(\frac{1}{9}\approx0.111\), \(\frac{1}{14}\approx0.071\) is between \(0\) and \(1\).

Step2: Calculate the sum of probabilities

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Answer:

E. No, because the sum of the probabilities of all possible outcomes is not 1.