Question: 2018 Winter Final - 18

You flip a fair red coin once, and you flip a fair blue coin once, independently of each other. Define the random variables

$X = \bigg\{$	$1\ $	if the red coin flip resulted in heads$,$
	$0\ $	if the red coin flip resulted in tails$,$
$Y = \bigg\{$	$1\ $	if the blue coin flip resulted in heads$,$
	$0\ $	if the blue coin flip resulted in tails$,$

and

• Z = $\min(X,Y).$

What is the expected value $\mathbb{E}(Z)$ of the random variable $Z$?