P(A or B)

P(A U B) is the same as P(A or B)!

The formula for either of two independent events occurring (a.k.a. "or" / "U") is:

P(A U B) = P(A) + P(B) - P(A ∩ B)

PRO TIP: We're subtracting away P(A ∩ B) because we don't want to double count for the overlap in these events both occurring at the same time.

What is the sample space (S) for all outcomes on a six-sided die?

S = {1, 2, 3, 4, 5, 6}

S_A = {1, 2, 3, 4, 5, 6}

Two out of the six potential outcomes fall in Event A...

P(A) = 2 / 6
P(A) = 1/3

S_B = {1, 2, 3, 4, 5, 6}

Three out of the six potential outcomes fall in Event B...

P(B) = 3 / 6
P(B) = 1/2

P(A ∩ B) = P(A) x P(B)
P(A ∩ B) = 1/3 x 1/2
P(A ∩ B) = 1/6

PRO TIP: This formula is only for independent events... and in this case: Event A does not impact the outcome of Event B. So we're good.

P(A U B) = 1/3 + 1/2 - 1/6
P(A U B) = 2/6 + 3/6 - 1/6
P(A U B) = 4/6
P(A U B) = 2/3

Answer: The probability of rolling a number greater than 4 or rolling an odd number is 2/3.