Decision Support Tools: Expected Value, Probability, and Computation of Probabilities

DECISION SUPPORT TOOLS
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Question 1
(a)The expected value is the average value that may be derived for an event whose outcomes
are probabilistic. Thus, it highlights an average estimation of the output based on the
respective probabilities associated with the outcomes. For a discrete probability
distribution, this may be computed by finding the respective probabilities of various
outcomes. Then the sum of the product of outcome and their respective probability is
computed for all the possible outcomes (Eriksson & Kovalainen, 2015).
A relevant example is known below (Flick, 2015).
(b) Daily sales of loaves of sourdough bread over the last 100 days
(1) The respective values in the column is shown below.
Normal view
Formula view
(1) The average daily sales
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E ( x ) =∑ x∗p ( x )
¿ ( 0∗0.05 ) + ( 1∗0.10 ) + ( 2∗0.25 )+ ( 3∗0.25 )+ ( 4∗0.20 )+ ( 5∗0.15 )
¿ 2.9
The average daily sales come out to be 2.9.
Excel output
(2) Probability of selling 2 or more loaves on a day
P ( x ≥ 2 )=P ( x=2 ) + P ( x =3 ) + P ( x =4 ) +P ( x=5 )
P ( x ≥ 2 )=0.25+0.25+ 0.20+0.15=0.85
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Probability of selling 2 or more loaves on a day would be 0.85.
(3) Probability of selling 3 or less loaves on a day
P ( x ≤ 3 ) =P ( x=0 ) + P ( x=1 ) + P ( x=2 ) + P ( x =3 )
P ( x ≤ 3 )=0.05+0.10+0.25+0.5=0.65
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