Question

HELP PLEASE

Suppose P(C | D) = 0.26, P(D) = 0.22, and P(D | C) = 0.17. What is P(C) Rounded to two decimal places?

A. 0.42
B. 0.34
C. 0.57
D. 0.68

Answer 1

Suppose P(C | D) = 0.26, P(D) = 0.22, and P(D | C) = 0.17. What is P(C) Rounded to two decimal places?

A. 0.42

B. 0.34

C. 0.57

D. 0.68

The answer is B.

Answer 2

All you need is the definition of conditional probability:

`P(A\mid B)=(P(A\cap B))/(P(B))`

So

`P(C\mid D)=(P(C\cap D))/(P(D))\iff0.26=(P(C\cap D))/(0.22)\implies P(C\cap D)=0.0572`

`P(D\mid C)=(P(C\cap D))/(P(C))\iff0.17=(0.0572)/(P(C))\implies P(C)\approx0.34`

and the answer would be B.