i need help on this question please what number represents the same amount as 6 hundreds+ 6 tens+ 14 ones?
2 answers:
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The tree diagram for the probability is shown below
P(Clay|Positive) is read 'Probability of Clay given the result is Positive'.
This is a case of conditional probability.
The formula for conditional probability is given as
P(Clay|Positive) = P(Clay∩Positive) ÷ P(Positive)
P(Clay∩Positive) = 0.21×0.48 = 0.1008
P(Positive) = P(Rock∩Positive) + P(Clay∩Positive) + P(Sand∩Positive)
P(Positive) = (0.53×0.53) + (0.21×0.48) + (0.26×0.75)
P(Positive) = 0.2809 + 0.1008 + 0.195
P(Positive) = 0.5767
Hence,
P(Clay|Positive) = 0.1008÷0.5767 = 0.175 (rounded to 3 decimal place)
P(Clay|Positive) is read 'Probability of Clay given the result is Positive'.
This is a case of conditional probability.
The formula for conditional probability is given as
P(Clay|Positive) = P(Clay∩Positive) ÷ P(Positive)
P(Clay∩Positive) = 0.21×0.48 = 0.1008
P(Positive) = P(Rock∩Positive) + P(Clay∩Positive) + P(Sand∩Positive)
P(Positive) = (0.53×0.53) + (0.21×0.48) + (0.26×0.75)
P(Positive) = 0.2809 + 0.1008 + 0.195
P(Positive) = 0.5767
Hence,
P(Clay|Positive) = 0.1008÷0.5767 = 0.175 (rounded to 3 decimal place)
Explanation:
Basically, you can do it in many ways. But just, in my opinion, exactly linear algebra was made for such cases.
the optimal way is to do it with Cramer's rule.
First, find the determinant and then find the determinant x, y, v, u.
Afterward, simply divide the determinant of variables by the usual determinant.
eg. and etc.
I think that is the best way to solve it without a hustle of myriad of calculations reducing it to row echelon form and solving with Gaussian elimination.