Question

Probability.
If X and Y are events of a trial with P(X)=1/2, P(X|Y')=2/3, P(X|Y)=3/7
find
P(Y)

Answer 1

Got it. P(Y)=7/10

Answer 2

how ?

Answer 3

Since \[P(X|Y')=\frac{ 2 }{ 3 }=\frac{ P(XintersectY') }{ P(Y') }\]
so P(Y')= 3/total
\[P(X|Y)=\frac{ 3 }{ 7 }=\frac{ P(XintersectY) }{ P(Y) }\]
P(Y)=7/total
We know P(Y)+P(Y')=1
7/total +3/total= 1
total =7+3=10
so P(Y)=0.7

Answer 4

I'd change the "total" to "sample space" to avoid confusion