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Probability : Interpretation of P(B|A) and P(B) and Comparison of Combination and Permutation

1. This week we were introduced to new terminology and symbols. Please interpret the symbol P(B|A) and explain what is meant by the expression. Why is P(B|A) not the same as P(B)?

2. Consider the formulas: nPr =n!/(n-r)! and nCr = n!/(n-r)!r!
a. Given the same values for n and r in each formula, which is the smaller value, P or C? n = 10 and r = 2.

nPr = n!/(n-r)! = 10! / (10 - 2)! = 90

nCr = n!/(n-r)!r! = 10! / (10 - 2)!2! = 45
Value C is smaller.

How does this relate to the concept of counting the number of outcomes based on whether or not order is a criterion?

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Interpretation of P(B|A) and P(B) and Comparison of Combination and Permutation are performed. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

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