Suppose P(C|D) =0.59, P(D) =0.44, and P (D|C) =0.38. What is P(C) rounded to two decimal places? A) 0.42 b) 0.57 c) 0.68 d) 0.34?
since
P(C|D) = P(C∩D)/P(D)
P(D|C) = P(C∩D)/P(C)
P(C∩D) = P(C|D)*P(D) = P(D|C)*P(C)
Now just plug in your numbers
To find P(C), we can use Bayes' theorem, which states that:
P(C|D) = (P(D|C) * P(C)) / P(D)
Given that P(C|D) = 0.59, P(D) = 0.44, and P(D|C) = 0.38, we can substitute these values into the equation:
0.59 = (0.38 * P(C)) / 0.44
To find P(C), we can rearrange the equation:
P(C) = (0.59 * 0.44) / 0.38
Calculating this expression:
P(C) ≈ 0.680
Rounded to two decimal places, the answer is 0.68.
Therefore, the correct answer is c) 0.68.