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## NPTEL Introduction to Machine Learning Assignment Answers Week 4

**Q1. A man is known to speak the truth 2 out of 3 times. He throws a die and reports that the number obtained is 4. Find the probability that the number obtained is actually 4:**

a. 2/3

b. 3/4

c. 5/22

d. 2/7

**Answer:** d. 2/7

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**Q2. Consider the following graphical model, mark which of the following pair of random variables are independent given no evidence?**

A. a,b

B. c,d

C. e,d

D. c,e

**Answer**: A. a,b

**Q3. Two cards are drawn at random from a deck of 52 cards without replacement. What is the probability of drawing a 2 and an Ace in that order?**

a. 4/51

b. 1/13

c. 4/256

d. 4/663

**Answer:** d. 4/663

**Q4.** **Consider the following Bayesian network. The random variables given in the model are modeled as discrete variables (Rain = R, Sprinkler = S and Wet Grass = W) and the corresponding probability values are given below.**

P(R) = 0.1

P(S) = 0.2

P(WR, S) = 0.8

P(WIR,S)= 0.7

P(WR, S) = 0.6

P(WR,S) = 0.5

Calculate P(S| W, R).

a. 1.

b. 0.5.

c. 0.22.

d. 0.78

**Answer:** c. 0.22

**Q5. What is the naive assumption in a Naive Bayes Classifier?**

a. All the classes are independent of each other

b. All the features of a class are independent of each other

c. The most probable feature for a class is the most important feature to be considered for classification

d. All the features of a class are conditionally dependent on each other.

**Answer:** b. All the features of a class are independent of each other

**Q6. A drug test (random variable T) has 1% false positives (ie., 1% of those not taking drugs show positive in the test), and 5% false negatives (i.e., 5% of those taking drugs test negative). Suppose that 2% of those tested are taking drugs. Determine the probability that somebody who tests positive is actually taking drugs (random variable D).**

a. 0.66

b. 0.34

c. 0.50

d. 0.91

**Answer:** a. 0.66

**Q7. It is given that P(A|B) = 2/3 and P(A|B) = 1/4. Compute the value of P(B|A).**

a. 1/2

b. 2/3

c. 3/4

d. Not enough information.

**Answer:** d. Not enough information.

**Q8. What is the joint probability distribution in terms of conditional probabilities?**

a. P(D1) * P(D2|D1) * P(S1|D1) * P(S2|D1) * P(S3|D2)

b. P(D1) * P(D2) * P(S1|D1) * P(S2|D1) * P(S3|D1, D2)

c. P(D1) * P(D2) * P(S1|D2) * P(S2|D2) * P(S3|D2)

d. P(D1) * P(D2) * P(S1|D1) * P(S2|D1, D2) * P(S3|D2)

**Answer:** d. P(D1) * P(D2) * P(S1|D1) * P(S2|D1, D2) * P(S3|D2)

**Q9. Suppose P(D1)=0.5. P(D2)=0.6. P(S1 D1)=0.4 and P(S1| D1′)=0.6. Find P(S1)**

a. 0.14

b. 0.36

c. 0.50

d. 0.66

**Answer **: c. 0.50

**Q10. In a Bayesian network a node with only outgoing edge(s) represents**

a. a variable conditionally independent of the other variables.

b. a variable dependent on its siblings.

c. a variable whose dependency is uncertain.

d. None of the above.

**Answer:** a. a variable conditionally independent of the other variables.

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