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AI & Data Mining/Week 3/Tutorial 3.md
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@@ -27,20 +27,25 @@
| High | 2/5 | 1/9 | Red | 3/5 | 2/9 | | | | | | | | |
# Problem 1
# $Pr[Diagnosis=N|E] = \frac{2}{5} \times \frac{2}{5} \times \frac{4}{5} \times \frac{3}{5} \times \frac{5}{14} = 0.027428571$
# $Pr[Diagnosis = B|E] = \frac{3}{9} \times \frac{4}{9} \times \frac{3}{9} \times \frac{3}{9} \times \frac{9}{14} = 0.010582011$
# $p(B) = \frac{0.0106}{0.0106+0.0274} = 0.2789$
# $p(N) = \frac{0.0274}{0.0106+0.0274} = 0.7211$
# $p(N) = \frac{0.0274}{0.0106+0.0274} = 0.7211$
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
@@ -48,4 +53,5 @@ Diagnosis B is much more likely than Diagnosis N
# Problem 3
# $Pr[Diagnosis = N|E] = \frac{0}{5} \times \frac{2}{5} \times \frac{4}{5} \times \frac{3}{5} \times \frac{5}{14} = 0$
# $Pr[Diagnosis = B|E] = \frac{5}{9} \times \frac{4}{9} \times \frac{3}{9} \times \frac{3}{9} \times \frac{9}{14} = 0.018$