Conditional Probability and its impact in probability calculation
Friends today we are going to learn about conditional probability and its impacts on probability calculations. First question arises is, what is a probability and how to solve math problems of probability.
In the college algebra we have a chapter on conditional probability, as we all know Probability is a way of telling or expressing a knowledge that an event will occur or has occurred and the probability of an event occurring given that another event has already occurred is called a conditional probability.
The Mathematical view of this comes with the following equation that an event A occurs, given that an event B is already occurred
P (B|A) = P (A and B) / P(A)
Baye’s Formula is another method through which we can solve or calculate a conditional probability. It states that the probability of event B is the sum of the conditional probabilities of event B given that event A has or has not occurred.
Mathematical expression for the following is:
P(B) = P(B|A)P(A) + P(B|Ac)P(Ac)
And for the two independent events (for event A and event B) the expression is:
P(B)P(A) + P(B)P(Ac) = P(B)(P(A) + P(Ac)) = P(B)(1) = P(B)
Let us consider an example for calculating a probability of getting an odd number on the dice.
Solution: dice has 6 faces each having a number written on it including 1,2,3,4,5 and 6, the number of odd number faces are (1,3,5)
If we have to calculate the probability of getting odd number we can calculate it in such way:
S = {1, 2, 3, 4, 5, 6} and A = {1, 3, 5}
as P(A) = number of probability of occurrence of event A/ total number of events
P(A) = 3/6 = .5 or ½
Let’s take another example which definitely going to answer all the doubts:
A card is drawn from an ordinary deck and we are told that it is red, what is the probability that the card is greater than 2 but less than 9.
Sol: let A= event of getting card is greater than 2 but less than 9.
B= event of getting red card.
Then we have to calculate P(A/B). In a Deck 26 are red and 26 are black cards.
Among red cards number of possible outcomes are 12 for A
Then P(A/B) = n(A intersection B)/n(B)= 12/26 = 6/12.
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