G4G0-2/AI & Data Mining/Week 3/Tutorial 3.md

Temperature	Skin	Blood Pressure	Blocked Nose	Diagnosis
Low	Pale	Normal	True	N
Moderate	Pale	Normal	True	B
High	Normal	High	False	N
Moderate	PaleFF	Normal	False	B
High	Red	High	False	N
High	Red	High	True	N
Moderate	Red	High	False	B
Low	Normal	High	False	B
Low	Pale	Normal	False	B
Low	Normal	Normal	False	B
High	Normal	Normal	True	B
Moderate	Normal	High	True	B
Moderate	Red	Normal	False	B
Low	Normal	High	True	N

	Temperature			Skin			Pressure			Blocked		Diag
	N	B		N	B		N	B		N	B	N	B
Low	2	3	Pale	1	3	Normal	1	6	True	3	3	5	9
Moderate	0	5	Normal	2	4	High	4	3	False	2	6
High	3	1	Red	2	2
	Temperature			Skin			Pressure			Blocked			Diag
Low	2/5	3/9	Pale	1/5	3/9	Normal	1/5	6/9	True	3/5	3/9	5/14	9/14
Moderate	0/5	5/9	Normal	2/5	4/9	High	4/5	3/9	False	2/5	6/9
High	2/5	1/9	Red	3/5	2/9

Problem 1

Pr[Diagnosis=N|E] = \frac{2}{5} \times \frac{2}{5} \times \frac{4}{5} \times \frac{3}{5} \times \frac{5}{14} = 0.027428571

Pr[Diagnosis = B|E] = \frac{3}{9} \times \frac{4}{9} \times \frac{3}{9} \times \frac{3}{9} \times \frac{9}{14} = 0.010582011

p(B) = \frac{0.0106}{0.0106+0.0274} = 0.2789

p(N) = \frac{0.0274}{0.0106+0.0274} = 0.7211

Diagnosis N is much more likely than Diagnosis B

Problem 2

Pr[Diagnosis = N|E] = \frac{2}{5} \times \frac{1}{5} \times \frac{3}{5} \times \frac{5}{14} = 0.0171

Pr[Diagnosis = B|E] = \frac{3}{9} \times \frac{6}{9} \times \frac{3}{9} \times \frac{9}{14} = 0.0476

p(N) = \frac{0.0171}{0.0171+0.0476} = 0.2643

p(B) = \frac{0.0474}{0.0476+0.0171} = 0.7357

Diagnosis B is much more likely than Diagnosis N

Problem 3

Pr[Diagnosis = N|E] = \frac{0}{5} \times \frac{2}{5} \times \frac{4}{5} \times \frac{3}{5} \times \frac{5}{14} = 0

Pr[Diagnosis = B|E] = \frac{5}{9} \times \frac{4}{9} \times \frac{3}{9} \times \frac{3}{9} \times \frac{9}{14} = 0.018