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Benchmark Six Sigma Expert View by Venugopal R Pascal's Triangle is named after the French Mathematician Blaise Pascal. It will look as depicted below: A quick examination about the Pascal’s triangle reveals the following: The top most row (referred to as 0th row) has one number, which is 1. The next row (first row) has two numbers (or two columns) and each number is the sum of the numbers of the boxes above from the previous row. The same practice continues, and we get the Pascal’s triangle. Thus if number on the nth row and kth column is represented as then: Let us look at an example of a simple binomial probability – the outcome of tossing a coin. The following table gives the number of tosses, the outcome and the numerical representation of each outcome combination The last column of the above table is emerging as the Pascal’s triangle. It may also be seen that the binomial probabilities for a particular outcome can be worked out. For example, let’s see the probability of obtaining exactly two heads, when the coin is tossed 4 times. The total number of possible outcomes is 1+4+6+4+1 = 16. The number of combinations that gave exactly two heads is 6. Hence the probability of obtaining exactly two heads is 6 /16 = 0.375 or 37.5%

Q 235. The Chinese “Seven multiplying squares” became the Pascal’s Triangle several centuries later and then gave rise to binomial theorem. Explain how these relate to some of the basics of probability. Note for website visitors - Two questions are asked every week on this platform. One on Tuesday and the other on Friday. All questions so far can be seen here - https://www.benchmarksixsigma.com/forum/lean-six-sigma-business-excellence-questions/ Please visit the forum home page at https://www.benchmarksixsigma.com/forum/ to respond to the latest question open till the next Tuesday/ Friday evening 5 PM as per Indian Standard Time The best answer is always shown at the top among responses and the author finds honorable mention in our Business Excellence dictionary at https://www.benchmarksixsigma.com/forum/business-excellence-dictionary-glossary/ along with the related term

The Pascal's triangle is an imaginary triangle in mathematics, that was discovered way back and used by mathematicians of different countries like India , Iran, China, Germany, Italy and finally highlighted by French mathematician Blaise Pascal, who is encredited with this phenomenon. It is applicable for binomial distributions and contains binomial coefficients, arranged in triangular array. It finds probability of events and combination of events. The sum of numbers in rows in Pascal triangle is given by 2n. Any probability evaluation, with two equally, independent and no predetermined order can be resolved , using Pascal’s triangle. The initial row of Pascal's triangle is conventionally designated as the 0 th row, n=0 at the top. The value of 0 th row is assigned as a non zero value and usually assigned as 1. The entries in each row are numbered from left and both extreme ends of a row are assigned values of 1. Each value entered in next row is the sum of value in the above and to the left with above and to the right. Example : A group of 10 people needs to be picked to create a committee of 4 people. We need to figure out the number of possible different committees of size 4 , that can be created from 10 people. While solving this issue, combination of people is important, not the mentioned order of the people. There will 10C4 possible committees. By scrutinizing, 10th row of Pascal's Triangle and selecting over to the 5th term (As first term is 10C0), it will give us the number of possible different committees. So we can conclude that there will be 210 possible committees of 4 people each, from a group of of 10 people. Applications of Pascal’s Triangle: - Algebra and probability - Graphic designers - Finance - Architect - Mapping