Greater than vs. Greater than or equal to

Question

Hello, I'm in an upper division probability class and we have to prove if:

P(x>3) = P(x>=4)

can anyone help me?

Answer 1

This question assumes a discrete sample space in which the out possible outcomes are natural numbers.

Since there are no possible outcomes between 3 and 4, the outcomes which are greater than 3 are 4 and any number greater than 4.

Example: Toss 5 coins. Enumerate the outcomes for # of heads greater than 3. Sure: 4 or 5.

Enumerate the outcomes for the # of heads greater than or equal to 4. Sure: 4 or 5