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A student S is suspected of cheating on exam, due to evidence E of cheating being present. Suppose that in the case of a cheating student, e
Question
A student S is suspected of cheating on exam, due to evidence E of cheating being present. Suppose that in the case of a cheating student, evidence E is present with 60% percent probability, and in the case of a student that does not cheat, evidence E is present with a 0.01 percent probability. Suppose also that the proportion of students that cheat is 1 percent. Show all the steps including identification of what formulas/properties you used. Points will be deducted from answers if only the final answer is provided.
Required:
a. Determine the events, given probabilities and inferred probabilities.
b. Determine the probability that the evidence is present.
c. Determine the probability that S cheated given the evidence is present.
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Mathematics
4 years
2021-08-13T04:20:41+00:00
2021-08-13T04:20:41+00:00 1 Answers
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Answer:
Step-by-step explanation:
Suppose we think of an alphabet X to be the Event of the evidence.
Also, if Y be the Event of cheating; &
Y’ be the Event of not involved in cheating
From the given information:
Thus,
P(Y’) = 1 – 0.01
P(Y’) = 0.99
The probability of cheating & the evidence is present is = P(YX)
The probabilities of not involved in cheating & the evidence are present is:
(b)
The required probability that the evidence is present is:
P(YX or Y’X) = 0.006 + 0.000099
P(YX or Y’X) = 0.006099
(c)
The required probability that (S) cheat provided the evidence being present is:
Using Bayes Theorem