### NPTEL Introduction To Machine Learning IITKGP ASSIGNMENT 4

**These are solutions for NPTEL Introduction To Machine Learning IITKGP ASSIGNMENT 4 Week 4**

Course Name: Introduction To Machine Learning IITKGP

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**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**

**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**

**These are solutions for NPTEL Introduction To Machine Learning IITKGP ASSIGNMENT 4 Week 4**

**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(W | R, S) P(WIR, P(WIR, P(WI-R.Calculate P(S | W, R).**

A. 1

B. 0.5

C. 0.22

D. 0.78

**Answer: C. 0.22 **

**These are solutions for NPTEL Introduction To Machine Learning IITKGP ASSIGNMENT 4 Week 4**

**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 (i.e., 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**

**These are solutions for NPTEL Introduction To Machine Learning IITKGP ASSIGNMENT 4 Week 4**

**Q7) It is given that P(A|B) = A. ½ 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: A. 1/2**

**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)**

**These are solutions for NPTEL Introduction To Machine Learning IITKGP ASSIGNMENT 4 Week 4**

**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: B. 0.36**

**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.**

**These are solutions for NPTEL Introduction To Machine Learning IITKGP ASSIGNMENT 4 Week 4**

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