Multiplication Theorem

Multiplication theorem is demonstrated as the possibility of the simultaneous and spontaneous events of both the events that are not dependent is provided by the good of their individual possibilities. A theorem is demonstrated as the formula or the logical statement in mathematics that is deduced or to be extrapolated from propositions or other formulas.  Addition and Multiplication theorem of probability are two separate terms that represent different formulas including “addition theorem of probability” and “multiplication theorem of probability”. The rule of probability demonstrates the event that is impossible which is equal to zero and the possibility of a particular event is equal to one. Hence, the possible range probabilities for event A are demonstrated as “0 ≤ P (A) ≤ 1”. Multiplication theorem utilises the particular calculation to measure the joint possibility.

Multiplication theorem of probability

The multiplication theorem of probability demonstrates the formula which represents that

• “P(A∩B) = P(A)×P(B|A) ; if P(A) ≠ 0”
• “P(A∩B) = P(B)×P(A|B) ; if P(B) ≠ 0”

“Multiplication theorem of probability” is in the subject of quantitative aptitude which is demonstrated as an integral and inseparable part of the exam of aptitude in India. “Multiplication theorem of probability” in the chapter on quantitative aptitude represents quantitative skills along with analytical and logical skills.

A solved instance of the “multiplication theorem of probability”

Considering the instance of an urn containing 10 blue balls and 20 red balls where the two balls are taken from the single bag one after another without any replacement. Now the probability that both balls will be checked that is drawn is considered to be red. In this case, A and B are considered to denote the particular event that the second and first balls are pinched as red balls. Now, the solution that needs to be measured is “P (AB)” or “P (A∩B)”. P (A) is equal to P (red balls in the first draw) which is equal to 20 divided by 30.

After this calculation, only 10 blue balls and 19 red balls are deserted in the bag. The possibility of getting a red ball in the second draw is also an instance of “conditional probability” where obtaining the second ball relies on getting off the first ball. Therefore, the “Conditional probability” of B on A is represented as “P (B|A) = 19/29”.

Thus, “multiplication theorem of probability” denotes

“P (A∩B) = P (A) × P (B|A)”= P (A ∩ B) = 20/30*19/29 = 38/87

Addition and multiplication theorem of probability: Overview

“Addition and multiplication theorem of probability” is represented in terms of the formula which represents that “P (AB) or P (A∩B) = Probability of occurring of collaborative A and B events”. “Additional theorem of probability” illustrates the two formulas where one or either of the “probability” of two exclusives “mutually events” occurring and another for “probability of exclusive two non-mutually events are occurring”. “Addition and multiplication theorem of probability” is utilised for computing the possibility of “A and B” and the possibility of “A or B” of two provided events A, and B described in the similar space of the sample. 

Facts of Multiplication theorem

• In the multiplication theorem, there is always a probability where two events are considered to be equal to the “product of the probability” to the other provided that the initial one has just emerged.
• The multiplication theorem was discovered “four thousand years ago” by “Babylonians”. In those times, they used to do the calculation of mathematics on “clay tablets”.

• Multiplication theorem or rule is used in probability to search the intersection of two distinct event sets termed “dependent” and “independent” events. The “independent events” are referred to when the event possible is not impacted by the prior event.

Conclusion

Theorems in mathematics not only assist in solving the problems of mathematics but the proofs are beneficial to improving in-depth comprehension of the underlying concepts. Quantitative aptitude generally means the individual’s capability to solve mathematical and numerical calculations. The significance of quantitative aptitude states that the person with logical thinking can be in a better position to make sense of and evaluate the data provided. Multiplication theorems in mathematics and quantitative aptitude are relatively different which means that multiplying the numbers is equal to the addition of equal groups.