Question

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 .

Answer 1

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

$Mean, μ = Ʃ[X.P(X)] = 1.2$

Variance $[Ʃ(X².P(X)) - μ²] = (2.2 - 1.2²)= 0.76$

$Standard \space deviation, σ = \sqrt{[Ʃ(X².P(X)) - μ²]} = \sqrt{(2.2 - 1.2²)} = 0.8718$