You roll a die.

Question

What is the probability if i roll a die and its odd or less than 5

Answer 1

Okay, this requires the addition rule for probability. You tend to use the multiplication rule for consecutive events and addition when the traits are simultaneous. The rule is:

P ( A or B) = P(A) + P(B) - P(A & B)

Specifically,

P (Odd OR 5) = P(Odd) + P(5) - P(Odd & 5)

Since 3 of the 6 sides are odd (1,3,5), you get:

P(Odd) = 3 / 6

There's only one 5, so:

P(5) = 1 / 6

Notice we counted "5" twice? That's why the rule has that odd ending. If the events can NOT overlap, it is zero and usually omitted. In this case,

P(Odd &5) = 1/6               (for the one extra count)

Finally, we get:

P(Odd OR 5) = 3/6 + 1/6 - 1/6   =  3/6 = 1/2

All done!