Probability

Probability is defined as the likelihood of an event occurring. Given that all the possible outcomes are equally likely, the probability of an event is equal to the number of favourable outcomes divided by the total number of possible outcomes, that is:

The probability of an event will be a number between 0 and 1. If the probability of an event is 0, then the event will never occur, that is, it is impossible. If the probability of an event is 1, then the event will occur, that is, it is a certainty.

Example:

A basket consists of 50 fruits, 15 apples, 20 oranges and 15 peaches.

(a)What is the probability of selecting an apple?

(b)What is the probability of selecting an orange?

(c)What is the probability of selecting a grape?

(d)What is the probability of selecting either an apple or an orange?

(e)What is the probability of selecting an apple, an orange or a peach?

Procedure:

-Determine the number of favourable outcomes.

-Determine the total number of possible outcomes.

-Divide the number of favourable outcomes by the total number of possible outcomes.

(a) The number of favourable outcomes = the number of apples, that is, 15.

The total number of possible outcomes = the number of fruits in the basket, that is, 50.

Therefore,

(b) The number of favourable outcomes = the number of oranges, that is, 20.

The total number of possible outcomes = the number of fruits in the basket, that is, 50.

Therefore,

(c) The number of favourable outcomes = the number of grapes, that is, 0.

The total number of possible outcomes = the number of fruits in the basket, that is, 50.

Therefore,

(d) The number of favourable outcomes = the number of apples and oranges, that is, 35.

The total number of possible outcomes = the number of fruits in the basket, that is, 50.

Therefore,

(e) The number of favourable outcomes = the number of apples, oranges and peaches, that is, 50.

The total number of possible outcomes = the number of fruits in the basket, that is, 50.

Therefore,

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