Question

To the nearest tenth, what is the value of P(C|Y)? 0.4 0.5 0.7 0.8

Answer 1

Answer:

P(C|Y) = 0.5.

Step-by-step explanation:

We are given the following table below;

               X             Y               Z             Total

A             32           10             28              70

B              6             5              25              36

C             18            15              7                40

Total       56           30            60              146

Now, we have to find the probability of P(C/Y).

As we know that the conditional probability formula of P(A/B) is given by;

                    P(A/B) =  $\frac{P(A \bigcap B)}{P(B)}$

So, according to our question;

P(C/Y) =  $\frac{P(C \bigcap Y)}{P(Y)}$

Here, P(Y) = $\frac{30}{146}$ and P(C $\bigcap$ Y) =  $\frac{15}{146}$  {by seeing third row and second column}

               

Hence, P(C/Y) =  $\frac{\frac{15}{146} }{\frac{30}{146} }$

                       =  $\frac{15}{30}$  = 0.5.