While the fundamental counting principle, permutations, and combinations deal with all possible combinations that can occur, probability deals with the likelihood of a specific event occurring.
For example, you know that when you toss a penny it is just as likely the penny will land heads up as it will land tails up. The penny has two sides, and each side is considered one part of the penny, or one half. Since both sides of the penny are one half of the penny (ignoring the rim of the penny), the probability of the penny landing heads up is the same as landing tails up.
The following is the probability of an event, A, happening:
The probability of an event happening is between 0 and 1, inclusive.
If an event has a probability of 0, it will likely never happen, and if an event has a probability of 1, it will almost certainly happen.
The probability of an event happening is between 0 and 1, inclusive. If an event has a probability of 0, it will likely never happen, and if an event has a probability of 1, it will almost certainly happen.
For example, if there is a bag that contains 7 blue marbles and no other marbles, and you pick a marble from the bag at random, what is the probability of the following two events:
Using the formula, we can see that:
Now let’s look at a slightly more complicated problem.
When you have two or more events occurring, calculating probability depends on the nature of the events. Independent events mean that the outcome of each event has no impact on the outcomes of the other events.
To find the final probability for two or more independent events, you simply find the product of the probabilities of each event.
On the other hand, dependent events mean that one event changes the outcomes of another event. In this case, you have to find the product of the probabilities while considering the impact of each event.
Probability of Independent Events
P(A) x P(B) = P(I)
Which says, "The probability of Event A happening independently from the probability of Event B happening equals the Probability of Independent Events happening."
Probability of Dependent Events
P(A1) x P(A2) = P(D)
Which says, "The probability of Event A2 happening, which is dependent on the Probabiliby of Event A1 happening equals the probability of the Dependent Events happening."
Answers to Practice Problems