Probability Of An Event

In an experiment, an event is the result that we are interested in.

The probability of an event A, written P(A), is defined as

Example:

When a fair dice is thrown, what is the probability of getting

a) the number 5

b) a number that is a multiple of 3

c) a number that is greater than 6

d) a number that is less than 7

Solution:

A fair die is an unbiased die where each of the six numbers is equally likely to turn up.

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

a) Let A = event of getting the number 5 = {5}

Let n(A) = number of outcomes in event A = 1

n(S) = number of outcomes in S = 6

b) Let B = event of getting a multiple of 3

Multiple of 3 = {3, 6}

c) Let C = event of getting a number greater than 6

There is no number greater than 6 in the sample space S.

C ={}

A probability of 0 means the event will never occur.

d) Let D = event of getting a number less than 7

Numbers less than 7 = {1, 2, 3, 4, 5, 6}

A probability of 1 means the event will always occur.

Example :

Each of the letters HELLO is written on a card. A card is chosen at random from the bag. What is the probability of getting the letter ‘L’?

Solution:

Since the card is randomly selected, it means that each card has the same chance of being selected.

S = {H, E, L ₁, L ₂, O} There are two cards with the letter ‘L’

Let A = event of getting the letter ‘L’ = {L ₁, L ₂}

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