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# Probability Examples

Probability is finding the possible number of outcomes of the event occurrence. It is assessed by considering the event's certainty as 1 and impossibility as 0. Here are few example problems with solutions on probability, which helps you to learn probability calculation easily.

## Probability Examples and Solutions

#### Example 1:

Let us consider an example: What is the probability of getting a 5 when a die is rolled and probability of not getting 5?

###### Solution:

Total Number of possible outcomes while rolling a die is 6. The number of ways, that a 5 occurs while rolling a die is 1. Hence We can calculate the Single Event Probability using the formula :

#### Single Event Probability Formula :

Probability of event A that occurs, P(A) = n(A) / n(S) Probability of event A that does not occur, P(A') = 1 - P(A)

Substituting the values in the formula, P(A) = 1/6 =0.167 Hence, the single event probability is 0.167 Probability of event A that does not occur, =1 - 0.167 = 0.833.

#### Example 2:

Let us consider an example when a pair of dice is thrown. Calculate the probability of getting odd numbers and even number together and the probability of getting only odd number. Find the conditional probability?

###### Solution:

The total number of possible outcomes of rolling a dice once is 6. Hence, the total number of outcomes for rolling a dice twice is (6x6) = 36.

The probability of getting an odd and even number is 18 and the probability of getting only odd number is 9. i.e., n(A) = 18 n(B) = 9

We can calculate the multiple event probability using the formula,

#### Multiple Event Probability Formula :

Probability of event A that occurs, P(A) = n(A) / n(S) Probability of event A that does not occur P(A') = 1 - P(A) Probability of event B that occurs P(B) = n(B) / n(S) Probability of event B that does not occur P(B') = 1 - P(B) Probability that both the events occur P(A ∩ B) = P(A) x P(B) Probability that either of event occurs P(A ∪ B) = P(A) + P(B) - P(A ∩ B) Conditional Probability P(A | B) = P(A ∩ B) / P(B)

Where, n(A) - Number of Occurrence in Event A, n(B) - Number of Occurrence in Event B, n(S) - Total Number of Possible Outcomes.

Substituting the values in the formula,

Therefore, the value of Multiple Event Probability are as follows: P(A) = 4 / 6 = 0.667. Hence, the Probability that event A occurs is 0.667 P(B) = 5 / 6 = 0.833. Hence, the Probability that event B occurs is 0.833 P(A') = 1 - P(A) = 1 - 0.667 = 0.333. Hence, the Probability that event A does not occur is 0.333 P(B') = 1 - P(B) = 1 - 0.833 = 0.167. Hence, the Probability that event B does not occur is 0.167 P(A ∩ B) = P(A) x P(B) = 0.667 x 0.833 = 0.556. Hence, the Probability that both the events occurs is 0.556 P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.667 + 0.833 - 0.556 = 0.944. Hence, the Probability that either of event occurs is 0.944 P(A | B) = P(A ∩ B) / P(B) = 0.556 / 0.833 = 0.667. Conditional probability of A given B is 0.667