Examples on Probability

Example 1: There are 6 pillows in a bed, 3 are red, 2 are yellow and 1 is blue. What is the probability of picking a yellow pillow?

Solution:

Probability is equal to the number of yellow pillows in the bed divided by the total number of pillows, i.e.

2/6 = 1/3

Example 2: There is a container full of coloured bottles, red, blue, green and orange. Some of the bottles are picked out and displaced. Sumit did this 1000 times and got the following results:

• No. of blue bottles picked out: 300
• No. of red bottles: 200
• No. of green bottles: 450
• No. of orange bottles: 50

a) What is the probability that Sumit will pick a green bottle?

For every 1000 bottles picked out, 450 are green.

Therefore,

P(green) = 450/1000 = 0.45

b) If there are 100 bottles in the container, how many of them are likely to be green?

Experiment implies that 450 out of 1000 bottles are green.

Therefore,

Out of 100 bottles, 45 are green.

Example 3: Find the probability of ‘getting 3 on rolling a die’.

Solution:

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

Total number of outcomes = n(S) = 6

Let A be the event of getting 3.

Number of favourable outcomes = n(A) = 1

i.e. A = {3}

Probability, P(A) = n(A)/n(S) = 1/6

Hence, P(getting 3 on rolling a die) = 1/6

Example 4: A vessel contains 4 blue balls, 5 red balls and 11 white balls. If three balls are drawn from the vessel at random, what is the probability that the first ball is red, the second ball is blue, and the third ball is white?

Solution:

Probability to get the first ball is red or the first event is 5/20

Since we have drawn a ball for the first event to occur, then the number of possibilities left for the second event to occur is 20 – 1 = 19

Hence, the probability of getting the second ball as blue or the second event is 4/19

Again with the first and second event occurring, the number of possibilities left for the third event to occur is 19 – 1 = 18

And the probability of the third ball is white or the third event is 11/18

Therefore, the probability is 5/20 x 4/19 x 11/18 = 44/1368 = 0.032

We can express it as: P = 3.2%.

Probability is defined as the likelihood of the occurrence of any event. Probability is expressed as a number between 0 and 1, where, 0 is the probability of an impossible event and 1 the probability of a sure event.

In this article on Basic Concepts of Probability, we will learn to predict Probability for an event likelihood and ranges from zero to one. It extends to distribution, which shows potential outcomes for random experiments. To find probability, determine the total possible outcomes.