Solving math problems with conditional probability
Today we are going to learn about the concepts behind Conditional Probability and How it helps to solve math problems. First question arises is that, what is a probability? It is a way of telling or expressing a knowledge that an event will occur or has occurred. The probability of an event occurring given that another event has already occurred is called a conditional probability. The Mathematical expressions 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)
The another method through which we can solve or calculate a conditional probability is Baye’s formula . 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)
Algebra equation is a mathematical equation in which one or both sides is an algebraic expression. For example 3x + 4y = 7z.
A card is drawn from an ordinary deck and we are told that it is black 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 black card.
Then we have to calculate P(A/B). In a Deck 26 are red and 26 are black cards.
Among black 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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