What is Probability?

By definition, Probability is the chance of an event happening at any point in time. In order to determine the probability of an event, we need to know the number of possible outcomes. Read More.

The study of Probability was first started in the 17^th century for analysing gambling games. By definition, Probability is the chance of an event happening at any point in time. There are many events whose outcomes cannot be predicted with certainty. When a coin is tossed, we can only tell how likely the chance of getting a ‘head’ than a ‘tail’ is. So, Probability is a field of Maths that tells the chances of one outcome happening over the other. It is also used in predicting the outcome of random experiments. In order to determine the probability of an event, we need to know the number of possible outcomes.

The Basic Formula of Probability

Probability of an event happening = Number of favourable results/Total number of options

If we take the example of tossing a coin, the toss has two possible outcomes, a head or a tail (H, T). So, the probability of a head is ½ and the Probability of a tail is also ½. Similarly, if we take the example of the roll of a dice, the total number of outcomes is 6 (1, 2, 3, 4, 5 and 6). So, the probability of getting any outcomes is 1/6.

Note that:

• When any event is sure to occur, it is called a certain event and the Probability is considered as 1.
• Any event that does not occur at all is said to have a Probability of 0.
• So, all other possibilities of an event occurring lies between 0 and 1 and cannot be negative.

It should also be kept in mind that Probability does not tell us the exact results of an event. It is just the guide to the possible outcomes. Now, Probability is used in various fields to study the possible outcomes. These include business decisions, insurance, medical tests, and the stock market. It is also used in telecom networks and the airline industry for the economical design of their networks and services.

Different Types of Probability Questions

Probability questions can be of different types:

1. Compound Probability

This is related to events A and B with their probabilities being P (A) or P (B).

So P (A or B) = P (A) + P (B) – P (A and B)

1. Mutually exclusive events

These events are related in such a way that when one occurs, the other does not occur. In other words, two such events cannot occur at the same time.

So, for such events, P (A and B) = 0.

Here, P (A and B) indicates the probability of the occurrence of events A and B at the same time.

Examples

Example 1: There are 6 balls in a bowl, 3 are red, 2 are yellow and 1 is blue. What is the probability of picking a yellow ball?

Solution:

The Probability is equal to the number of yellow balls in the bowl divided by the total number of balls, i.e. 2/6 = 1/3.

Example 2: A die is rolled, find the probability that an even number is obtained.

Solution:

Let us first write the possible number of outcomes for the event in the sample space S
S = {1, 2, 3, 4, 5, 6}

Let E be the event "an even number is obtained" and E includes the following
E = {2, 4, 6}

So, by applying the formula of classical Probability:
P (E) = n (E) / n(S) = 3 / 6 = 1 / 2

Example 3: What is the probability of getting a 2 or a 5 when a die is rolled?

Solution:

The individual Probability of getting a 2 or a 5 is 1/6.

So, by applying the formula of compound Probability,

Probability of getting a 2 or a 5 is,

P (2 or 5) = P (2) + P (5) – P (2 and 5)

=1/6 + 1/6 – 0

=2/6 = 1/3.

Example 4: Two coins are tossed, find the Probability that two heads are obtained.

Note: Each coin has two possible outcomes H (heads) and T (Tails).

Solution:

The possible outcome is denoted by the sample space S.

S = {(H, T), (H, H), (T, H), (T, T)}

Let E be the event "two heads are obtained".

E = {(H, H)}

We use the formula of the classical Probability.

P (E) = n (E) / n(S) = 1 / 4

Common Mistakes to Avoid While Solving Probability Questions

Let us look into some of the common mistakes while solving Probability related questions:

• Many of us do not write down the total outcome of the event and also the formula. The best practice is to write down the total outcomes, favourable outcomes and the formula, and then calculating the Probability.
• In many cases, we make a mistake in counting the number of outcomes in the case of cards. For card-related questions, it is important to note the number of cards in a pack, the number of each individual card, and the number of each type of card.

Some of us also tend to get confused between mutually-exclusive events and independent events. So, clearly differentiating between these events is important.

Note: The sample questions have been sourced from:

Yahoo
Simple and Fun Maths
Cyberforum.com
Chegg.com
Studypool.com
YouTube
Analyzemath.com

Read More:

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• Banking Exam Data Interpretation Guide