Rebecca is playing a game that involves rolling a fair $4-$sided die and a fair $6-$sided die.

a$.$ Construct the sample space. How many possible outcomes are in the sample space?

b$.$ You win the game if the values on the dice match. Compute the probability of winning $($success$).$ Round to three decimal places.

c$.$ Compute the probability of losing $($failure$).$ Round to three decimal places.

d$.$ You and Rebecca play $3$ rounds of the game. Compute the probability of winning in all three rounds of the game. Round to four decimal places.

e$.$ You and Rebecca play $3$ rounds of the game. Compute the probability of losing at least one round of the game. Round to four decimal places.