We've discussed the probability of simple events in a previous article. A simple event is basically just one event and determining its probability is usually straight forward. It is often that we need to know the probability of more than one event occurring. For example, what is the probability of getting heads or tails when flipping a coin? One event is getting the heads showing face up, and the other event is getting tails showing face up. Since the only two outcomes here are heads or tails, we would have a 100% chance of getting a head or tails.
How did we get the result of 100%? The first event of getting heads has a probability of 1 divided by 2, or 0.5. The second event has a probability of 1 over 2, and also has a probability of 0.5. It follows than the probability of getting heads or tails, is the probability of the getting heads plus the probability of getting a tails which is 0.5 plus 0.5 or 1.0 which is 100%.
If we have a deck of playing cards, it has 52 cards, with four suites, and 13 cards to a suite, what would be the probability of randomly drawing an ace or a king? Following the last example, it would be the probability of the first event, getting ace, plus the probability of the other event, getting a king. There are four ways of getting an ace out of 52 possible outcomes making the probability of getting an ace 1 over 13. There are also four ways of getting a king, out of a possible 52 outcomes for a probability of 1 over 13. So the probability of getting an ace or a king is 2 over 13, the sum of the two probabilities. It is important to note these two events are mutually exclusive. This means that getting an ace and a king on the same card is not a possible outcome.
What is the probability of drawing one ace out of the deck, or a black card? Remember that two of the suites are black for a total of 26 black cards. As in the previous example we need the probability of the first event, drawing an ace, and that is 4 over 52. The probability of drawing a black card is 26, the number of ways of drawing a black card, divided by 52, the total number of outcomes, which is one half. That would make the probability of getting an ace or a black card 4 over 52, plus 26 over 52, for a probability of 30 over 52.
This probability of 30 over 52 is NOT correct. The reason is that these two events are NOT mutually exclusive. Two of the aces are also black, which means that getting an ace and a black card at the same time is a possible outcome. In the above calculation we counted the outcome of a black ace twice. The probability of drawing a card that is an ace and a black card must be subtracted from the above result. So the probability of getting a black ace is 2 out of 52 possible outcomes, making the probability of getting an ace or a black card, 30 over 52, minus 2 over 52, for a result of 28 over 52, or 7 over 13.
