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