A consumer electronics company is considering marketing a new model of TV screen. In the past 40% of the TV screens marketed by
the company have been successful. Before marketing the latest screen, the marketing research department conducts an extensive study. The report will be either favorable or unfavorable to the introduction. In the past, 80% of the successful TV screens had gotten a favorable report, and 30% of the unsuccessful screens had gotten a favorable report.
1. What are the prior probabilities (use unconditional probability notation)?
2. What are the given conditional probabilities (use conditional probability notation)?
3. What is the resulting probability tree? (see video lecture. Your book uses a table. They are equivalent, but the tree is shorter and more mechanical to implement.)
4. Use the tree above to find the probability that the new screen will be successful if the marketing research issues a favorable report. (hint: put all the English wording into notation. They will involve conditional probabilities. Use the definition of conditional probability and the tree to find the necessary conditional probabilities).
5. Use the tree above to find the probability that the new screen will be successful if the marketing research issues an unfavorable report? Use the probability tree above to work out your answer.
1. What are the prior probabilities (use unconditional probability notation)?
2. What are the given conditional probabilities (use conditional probability notation)?
3. What is the resulting probability tree? (see video lecture. Your book uses a table. They are equivalent, but the tree is shorter and more mechanical to implement.)
4. Use the tree above to find the probability that the new screen will be successful if the marketing research issues a favorable report. (hint: put all the English wording into notation. They will involve conditional probabilities. Use the definition of conditional probability and the tree to find the necessary conditional probabilities).
5. Use the tree above to find the probability that the new screen will be successful if the marketing research issues an unfavorable report? Use the probability tree above to work out your answer.
1 answer:
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Answer:
y = 11 x
Explanation:
The relationship between two variables x,y is said to be a proportional relationship if the ratio between the values of the two variables is constant:
(3)
where k is the a constant value valid for all pairs (x,y).
In this problem, we are told that Charmaine earns $11 per hour. Here we call:
y = amount of money earned
x = time
We can see that the relationsip between x and y is proportional. In fact:
- after 1 hour, Charmaine has earned $11 (1)
- after 2 hours, Charmaine has earned $22 (2)
.. and so on
For (1), we find
so k = 11
For (2), we find
so k = 11
So, k = 11 for every pair (x,y), so the two variables have proportional relationship.
Moreover, we can write an equation that relates the two variables re-arranging eq.(3).