Question

Suppose P(A)=0.44, P(B)=0.22, P(C)=0.34, P(D/A)=0.106, P(D/B)=0.106, P(D/C)=0.035. Calculate P(A/D).

a) 0.48
b) 0.32
c) 0.24
d) 0.56

Answer 1

To calculate P(A|D), use Bayes' theorem, substituting the given probabilities into the formula to find the precise value. First calculate P(D) using the law of total probability, then substitute back into the Bayes' theorem formula to get P(A|D).

Step-by-step explanation:

To find P(A|D), we use Bayes' theorem which relates the probability of event A given event D has occurred to the probability of D given A, the probability of A, and the probability of D. Bayes' theorem formula is P(A|D) = P(D|A)P(A) / P(D). The probability of D, P(D), can be found using the law of total probability, which in this case is P(D) = P(D|A)P(A) + P(D|B)P(B) + P(D|C)P(C). Plugging in the given values:

P(D) = (0.106)(0.44) + (0.106)(0.22) + (0.035)(0.34)

Once we calculate P(D), we can use it in the Bayes' theorem formula to find P(A|D):

P(A|D) = P(D|A)P(A) / P(D)

P(A|D) = (0.106)(0.44) / P(D)

After completing the calculation, you find the correct option that matches the calculated probability.