Th e Steiner-Wallace Corporation has determined that itneeds to expand in order to accommodate growing demandfor its laptop computers. Th e decision has come down to eitherexpanding now with a large facility, incurring additional costs andtaking the risk that the demand will not materialize, or expandingsmall, knowing that in three years management will need toreconsider the question.Management has estimated the following chances for demand:• Th e likelihood of demand being high is 0.60.• Th e likelihood of demand being low is 0.40.Profi ts for each alternative have been estimated as follows:• Large expansion has an estimated profi tability of either$100,000 or $60,000, depending on whether demand turnsout to be high or low.• Small expansion has a profi tability of $50,000, assuming thatdemand is low.• Small expansion with an occurrence of high demand wouldrequire considering whether to expand further. If thecompany expands at that point, the profi tability is expectedto be $70,000. If it does not expand further, the profi tabilityis expected to be $45,000.(a) Draw a decision tree showing the decisions, chanceevents, and their probabilities, as well as the profi tabilityof outcomes.(b) Solve the decision tree and decide what Steiner-Wallaceshould do.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Th e Steiner-Wallace Corporation has determined that it
needs to expand in order to accommodate growing demand
for its laptop computers. Th e decision has come down to either
expanding now with a large facility, incurring additional costs and
taking the risk that the demand will not materialize, or expanding
small, knowing that in three years management will need to
reconsider the question.
Management has estimated the following chances for demand:
• Th e likelihood of demand being high is 0.60.
• Th e likelihood of demand being low is 0.40.
Profi ts for each alternative have been estimated as follows:
• Large expansion has an estimated profi tability of either
$100,000 or $60,000, depending on whether demand turns
out to be high or low.
• Small expansion has a profi tability of $50,000, assuming that
demand is low.
• Small expansion with an occurrence of high demand would
require considering whether to expand further. If the
company expands at that point, the profi tability is expected
to be $70,000. If it does not expand further, the profi tability
is expected to be $45,000.
(a) Draw a decision tree showing the decisions, chance
events, and their
of outcomes.
(b) Solve the decision tree and decide what Steiner-Wallace
should do.
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