Q9
A student answers a multiple-choice examination question that offers four possible
answers. Suppose the probability that the student knows the answer to the question is
8 and the probability that the student will guess is .2. Assume that if the student
guesses, the probability of selecting the correct answer is .25. If the student correctly
answers a question. what is the probability that the student really knew the correct
answer?
Q 10
The probability distribution for a random variable Y is given in table. Find the mean.
variance, and standard deviation of Y .
Q9
This is a case of the Bayes theorem
Let B1 denote the event that the student knows the answer
and B2 denote the event that the student guesses the answer
Let A denote the event that the student correctly answer
Given "P(B_1)= 0.8"
"P(B_2)=0.2"
"P(A\/B1)=1"
P(A/B2)= 0.25
We have to find P(B1/A)=
="\\frac{0.8*1}{[0.8*1+0.2*0.25]}"
"=\\frac{0.8}{[0.8+ 0.05]}"
"=\\frac{0.8}{0.85}"
= 0.9412
Therefore Required Probability is 0.9412
Q10
"Mean, \u03bc = \u01a9[X.P(X)] = 1.2"
Variance "[\u01a9(X\u00b2.P(X)) - \u03bc\u00b2] = (2.2 - 1.2\u00b2)= 0.76"
"Standard \\space deviation, \u03c3 = \\sqrt{[\u01a9(X\u00b2.P(X)) - \u03bc\u00b2]} = \\sqrt{(2.2 - 1.2\u00b2)} = 0.8718"
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