Question

Find P(C|Y) from the information in the table.

To the nearest tenth, P(C|Y) =

Answer 1

Answer:0.5

Explanation:

Answer 2

From the definition of conditional probability,


`\mathbb P(C\mid Y)=(\mathbb P(C\cap Y))/(\mathbb P(Y))`

and by the law of total probability,


`\mathbb P(Y)=\mathbb P(Y\cap A)+\mathbb P(Y\cap B)+\mathbb P(Y\cap C)`

In other words, each cell in the grid left of and above the total column and row represents the joint probabilities (e.g.
`\mathbb P(X\cap A)=(32)/(146)`). So,


`\mathbb P(C\mid Y)=(15)/(30)=\frac12=0.5`