If we are to take the contextual independence into account, we need to consider the dependence between FH and MH when both FB and MB are true (in which case FT and MT are irrelevant). For all of the other contexts, we can treat FH and MH as independent. The algorithm CVE does this automatically.

The conditional probabilities of Figures 6 and 7 can be represented as the following confactors:

fb,

FH OT *Value*

![0_image_1.png](0_image_1.png)

true true p1 true false p2 ![0_image_0.png](0_image_0.png) false false 1 − p2


$$(33)$$

FH FT *Value*

![0_image_2.png](0_image_2.png)

![0_image_3.png](0_image_3.png)

![0_image_5.png](0_image_5.png)

true true p3 true false p4 false true 1 − p3 false false 1 − p4

![0_image_4.png](0_image_4.png)

$$(34)$$

mb,

MH MT *Value*

true true p7

true false p8 false true 1 − p7 false false 1 − p8

![0_image_7.png](0_image_7.png)

$$(36)$$

| false   | false   | 1 − p6   |
|---------|---------|----------|
| MH      | MT      | Value    |
| true    | true    | p7       |
| true    | false   | p8       |
| false   | true    | 1 − p7   |
| false   | false   | 1 − p8   |
| mb, OT  | S       | Value    |
| true    | true    | p9       |
| true    | false   | p10      |
| false   | true    | 1 − p9   |
| false   | false   | 1 − p10  |

MH OT *Value*

![0_image_6.png](0_image_6.png)

![0_image_8.png](0_image_8.png)

![0_image_9.png](0_image_9.png)

true true p5 true false p6 false true 1 − p5 false false 1 − p6

$$(35)$$

$$(37)$$

Eliminating OT from these confactors results in six confactors:

| fb ∧ mb,   |
|------------|

| true   | true   | true   | p9 ∗ (p5 ∗ p1) + (1 − p9) ∗ (p6 ∗ p2)                           |
|--------|--------|--------|-----------------------------------------------------------------|
| true   | true   | false  | p10 ∗ (p5 ∗ p1) + (1 − p10) ∗ (p6 ∗ p2)                         |
| true   | mbalse | true   | p9 ∗ ((1 − p5) ∗ p1) + (1 − p9) ∗ ((1 − p6) ∗ p2)               |
| true   | mbalse | false  | p10 ∗ ((1 − p5) ∗ p1) + (1 − p10) ∗ ((1 − p6) ∗ p2)             |
| false  | true   | true   | p9 ∗ (p5 ∗ (1 − p1)) + (1 − p9) ∗ (p6 ∗ (1 − p2))               |
| false  | true   | false  | p10 ∗ (p5 ∗ (1 − p1)) + (1 − p10) ∗ (p6 ∗ (1 − p2))             |
| false  | false  | true   | p9 ∗ ((1 − p5) ∗ (1 − p1)) + (1 − p9) ∗ ((1 − p6) ∗ (1 − p2))   |
| false  | false  | false  | p10 ∗ ((1 − p5) ∗ (1 − p1)) + (1 − p10) ∗ ((1 − p6) ∗ (1 − p2)) |

fb,