One fair die is rolled. What is the probability of getting an even number?

When a fair die is rolled, there are 6 outcomes: 1,2,3,4,5,6. As 2,4, or 6 are even, the probability of getting an even number is
3/6=1/2

A card is selected at random from an ordinary 52-card deck. What is the probability that it is a heart?

In an ordinary 52-card deck, there are 13 hearts. Hence, the probability that it is a heart is 13/52=0.25

In the Maryland Cash In Hand game, to win the grand prize the contestant must match seven distinct numbers, in any order, among the numbers 1 through 31 randomly drawn by a lottery representative. What is the probability of choosing the winning numbers?

Since there are unique SEVEN(7) distinct winning numbers among 1-31, and there are C(31, 7)=31!/(7!*24!)=2629275 combinations of 7 numbers. So,
the probability of choosing the winning numbers is
1/2629275=0.00000038