This problem is a very basic and cute application of set theory, Venn diagram and AM GM inequality to solve the ISI MStat 2016 PSB Problem 3.
For any two events and
, show that
P(region Red) =
P(region Blue) =
P(region Grey) =
P(region Brown) =
Observe that .
.
.
.
.
.
.
.
Observe that .
by AM - GM Inequality.
.
.
Hence,
This problem is a very basic and cute application of set theory, Venn diagram and AM GM inequality to solve the ISI MStat 2016 PSB Problem 3.
For any two events and
, show that
P(region Red) =
P(region Blue) =
P(region Grey) =
P(region Brown) =
Observe that .
.
.
.
.
.
.
.
Observe that .
by AM - GM Inequality.
.
.
Hence,