Answer:
The probability is 0.18
Step-by-step explanation:
Here, we are interested in calculating a conditional probability;
Let the event that a voter is a Republican be R , the event that a voter is a Democrat be D and that a voter is an independent is I
Let the event that the election issue is favored be F
We have the following probabilities;
P(R) = 46% = 0.46
P(D) = 45% = 0.45
P(I) = 1-0.45-0.46 = 0.09
The conditional probability we want to calculate is;
P(D | F) which can be read as probability of event D given event F
From the question, we can identify the following conditional probabilities;
P(F|R) = 0.46 * 0.5 = 0.23 (0.5 is gotten from 50% = 50/100)
P(F | D) = 0.45 * 0.4 = 0.18
P( F | I) = 0.09 * 0.6 = 0.054
P(F) = 0.054 + 0.18 + 0.23 = 0.464
Mathematically; From Baye’s theorem
P( D | F) ={ P ( F | D) * P(D) }/ P(F)
P( D | F) = (0.18 * 0.45)/0.464 = 0.1745
