Probability Examples

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Probability is the section of mathematics which involves the study of the possibility of an event occurring or not occurring in a given particular situation. Probability of an event ranges from ‘0’ (which implies that it is impossible for the event to happen) to ‘1’ (which implies that the event will happen). In order to find the chances of a particular event to occur, we have to consider its chances compared to the total possible outcomes for that event and then find the probability of that event.

Example 1: What is the probability of getting the number ‘5’ when a fair die is rolled?
In order to find the probability when a fair die is rolled, we should first look at the total possible outcomes for this event.
Total possible outcomes = {1, 2, 3, 4, 5, 6} ==>implies that there is a possibility for any of these 6 numbers to occur.
Out of these outcomes the chances of getting only the number ‘5’ is 1 out of 6.
Therefore P(E) = 1/6

Example 2: If a coin is tossed and then a fair die is rolled, what is the probability of getting ‘heads’ and a ‘4’?

When a coin is tossed the possible outcome is heads or tails==>which implies ‘2’ outcomes.
Hence, chances of getting a heads= 1/2.
Similarly, when a fair die is rolled, there is a possibility of getting {1, 2, 3, 4, 5, 6} for any of these 6 numbers to occur.
Hence, the chances of getting a ‘4’= 1/6.
Therefore, the Probability (of getting ‘heads’ and a ‘4’) = 1/2 * 1/6 = 1/12.