How to Find Probability of Two Events

Probability comes into application in the fields of physical sciences, commerce, biological sciences, medical sciences, weather forecasting, etc. As far as the JEE exam is concerned, probability is an important topic. Probability refers to the occurrence of a random event. It is used to predict how likely the events will happen. In this article, we will see how to find the probability of two events.

When Events are Independent

When the outcome of the first event does not influence the outcome of the second event, those events are called independent events. To determine the probability of two independent events we have to multiply the probability of the first event by the probability of the second event.

If A and B are two independent events, then the probability of both happening is given by the equation P(A and B) = P(A)×P(B).

Example

Two dice, one coloured green, and one coloured red are thrown. Find the probability that the score on the red die is 3 and green die is 1.

Solution:

Probability of score on red die is 3 = 1/6

Probability of score on the green die is 1 = 1/6

The probability that red shows 3 and green shows 1 = 1/6 x 1/6 = 1/36

Hence the required probability is 1/36.

When Events are Dependent

When the outcome of the first event influences the outcome of the second event, those events are called dependent events.

If A and B are two dependent events, then P(A and B) = P(A)×P(B/A). P(B/A) denotes the probability of B, once A has happened.

Example

What is the probability for you to choose two black cards in a deck of cards?

Solution:

There are 26 red and 26 black cards in a deck of cards.

Probability of choosing a black card at random = 26/52 = 1/2

Probability of choosing a black card again = 25/51

Required probability = 1/2 × 25/52 = 25/104

When Events are Mutually Exclusive

Two events are said to be mutually exclusive when they cannot happen at the same time. The probability that one of the mutually exclusive events occur is given by the sum of their individual probabilities.

If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)

Example

A die is tossed. Find the probability of the die showing a number 2 or number 5?

Solution:

Probability of getting 2 = 1/6

Probability of getting 5 = 1/6

Probability of getting 2 or 5 = 1/6 + 1/6 = 2/6 = 1/3

Hence the required probability is 1/3.

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