Probability

Today we learned about probability. This is very useful when trying to determine the chance of an event occurring. The probability of an event E occurring is P(E). This can be calculated in different ways depending on the problem itself. Here is an example based on one I saw on http://www.mathsisfun.com/data/probability.html:

A person is rolling two dice and wants to determine the probability of rolling a double, in which the numbers on both dice are the same.

There are only 6 possible outcomes in which the dice are doubles:

{1, 1}, {2, 2}, {3, 3}, {4, 4}, {5, 5}, {6, 6}

The sample space, or set of all possible outcomes contains 36 possible outcomes:

{1, 1}, {1, 2}, {1, 3}, {1, 4}, . . . {6, 3}, {6, 4}, {6, 5}, {6, 6}

Therefore, the chance of rolling doubles is given by:

6 / 36 = 1 / 6 = 0.167 = 16.7%

The probability of any event occurring can only be within the range of 0-1. An event whose probability is 0, or 0%, is called impossible, while an event whose probability is 1, or 100%, is called certain.

An independent event is one whose outcome is not affected by those of other events. An example of this would be flipping a coin; the probability is always 1 / 2 = 0.5 = 50%.
A dependent event is one whose outcome is affected by those of other events. An example of this would be drawing cards from a deck. After the first card is drawn, there is one fewer card in the deck.