The following example was provided in class shown in picture

The following example was provided in class, shown in picture 1.

On picture 2 the problem is already set up but need help coming up with the equations in order to determine the matrix and find the probability of each.

Solution

The following equation for this problem is

55% are republicans, 45% democart

P(R)=0.55

P(D)=0.45

P(E₁)+P(E₂)+P(E₃)+P(E₄)=0.55................(0)

P(E₅)+P(E₆)+P(E₇)+P(E₈)=0.45................(1)

2P(R|V)=3P(D|V)

2P(E₁)=3P(E₅)...................2

5P(R|L)=7P(D|L)

5P(E₃)=7P(E₇)........................3

P(E₁)+P(E₅)=0.22..........................4

P(E₂)+P(E₆)=0.09..........................5

P(E₃)+P(E₇)=0.37...........................6

P(E₈)+P(E₄)=0.32............................7

From 2 and 4

P(E₅)=0.088,P(E₁) =0.132

From 3 and 6

P(E₇)=0.2642, P(E₃)=0.1057

From 1

P(E₆)+P(E₈)=0.0977

From 0

P(E₂)+P(E₄)=0.3122