Suppose there is a well-shuffled deck of cards, and you randomly select one card. Then what is the chance that you pick a second card that is not of the same suit or number? For example, if the first card is an ace of spades, the second can’t be an ace or a spade.
Such problems are better solved using the complementary rule, i.e., estimate the probability of choosing the same number or same suit and then subtract it from 1. Pick the first card. The probability of picking the second card carrying the same number = remaining number of cards displaying the same number / total remaining cards = 3/51. Similarly, the chance of picking a card of the same suit = the remaining number of the same suit / total remaining cards = 12/51.
The probability of taking out either the same number OR the same suit is the sum of the probabilities (the OR rule), i.e., 15/51. The required probability is 1- 15/61 = 36/51 = 0.706
