$A$
rolls one die. Player $B$
rolls two dice. If $A$
rolls a number greater or equal to the largest number rolled by $B$
, then $A$
wins, otherwise $B$
wins. What is the probability that B wins?

 You roll a die 3 times. What is the probability that at least one roll is greater than 2?
 You roll two dice. What is the probability that their sum is less than 7?
 A coin is flipped 3 times, displaying either heads (
$H$
) or tails ($T$
). What is the probability that you do not get$\text{H H H}$
?

Let
$a$
represent the number rolled by$A$
. What is the probability that$B$
wins in terms of$a$
? 
$A$
wins if both of$B$
's dice roll are smaller than$a$
. 
Consider the scenario from the previous hint. What is the probability that
$B$
does not win for a given$a$
? 
How may we map the expression from the previous hint to all possible
$a$
?

Let
$a \in \{1,2,3,4,5,6\}$
represent the number rolled by$A$
.$B$
wins if at least one of$B$
's rolls is higher than$a$
. This would be$1$
minus the probability that both of$B$
's rolls are smaller than or equal to$A$
's.For a given
$a$
, there exists$a$
numbers smaller or equal to$a$
that may be rolled. Therefore, for a given$a$
the probability of$B$
winning is$1(\frac{a}{6})^2$
. Now, consider all possible values of$a$
. The probability of any value of$a \in \{1,2,3,4,5,6\}$
being rolled is$\frac{1}{6}.$
So, the overall probability that$B$
wins is$\sum_{a=1}^{6} \frac{1}{6}\big(1(\frac{a}{6})^2\big) = \frac{125}{216}.$
See properties of summations here to aid in evaluating the sum.