Formula for classical probability

Classical probability uses sample spaces to determine the numerical probability that an event will happen.

Classical probability assumes that all outcomes in the sample space are equally likely to occur. For example, when a single die is rolled, each outcome has the same probability of occurring. Since there are six outcomes, each outcome has a probability of 1/6. When a card is selected from an ordinary deck of 52 cards, we assume that the deck has been shuffled, and each card has the same probability of being selected. In this case, it is 1/52.

Definition:

If the sample space S contains n equally likely basic outcomes and the event A consists of m of these outcomes , then

In words, “The probability of event A equals to number of basic outcomes in A, divided by the total number of outcomes in the sample space”.

We can write definition above as .

Example:

For a card drawn from an ordinary deck find the probability of getting a queen

Solution:

Let A - be an event getting a queen. Since there are four queens then . Hence, .

Example:

Find the probability of obtaining an even number in one roll of a die.

Solution:

In this experiment S= {1, 2, 3, 4, 5, 6}.Let A - be an event that an even number is observed on the die. Event A has three outcomes: 2, 4, and 6.

If any one of these three numbers is obtained, event A is said to occur. Hence,

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