Nine cards are numbered 1-9. what is the probability of drawing a number greater than 6 or an odd number.

You can rewrite this such that the "OR" applies to mutually exclusive possibilities, and then you can add up the proababilities.

The probabilitity of drawing an odd number or a number larger than 6, is the same as drawing one of the odd numbers smaller than 6, or a number larger than 6. The OR now refers to mutually exclusive possibilitities and you can then add up the probabilities for them as there is no double counting.

Clearly there are 6 numbers that satisfy the criterium, so the probablity is 6/9 = 2/3.

YOu can also handle "OR" diurectly using the principle of exclusion and inclusion using the formula:

N[A OR B] = N[A] + N[B] - N [A AND B]

There are 3 numbers larger than 6, there are 5 odd numbers and there are 2 numbers that are larger than 6 nd odd. There are thus 3 + 5 - 2 = 6 numbers that are larger than 6 or odd.