| 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

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

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