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Tebygolrwydd Cyflawn

Tebygolrwydd Cyflawn. Rheol 6 P(B) = P(B |A 1 )P(A 1 ) + P(B |A 2 )P(A 2 ) + ……+ P(B |A r )P(A r ). Enghraifft

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Tebygolrwydd Cyflawn

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  1. Tebygolrwydd Cyflawn Rheol 6 P(B) = P(B|A1)P(A1) + P(B|A2)P(A2) + ……+ P(B|Ar)P(Ar) • Enghraifft • Bob dydd mewn ffatri cynhyrchir 40% o gydran benodol ar beiriant A, 10% ar beiriant B a 50% ar beiriant C. Mae 60% o’r cydrannau a gynhyrchir ar beiriant A yn goch ac mae 40% yn wyrdd. Mae 30% o’r cydrannau a gynhyrchir ar beiriant B yn goch ac mae 70% yn wyrdd. Mae 50% o’r cydrannau a gynhyrchir ar beiriant C yn goch ac mae 50% yn wyrdd. • Cyfrifwch y tebygolrwydd fod cydran a ddewisir ar hap o blith yr holl gynnyrch dyddiol yn wyrdd. • O wybod bod y gydran yn wyrdd, cyfrifwch y tebygolrwydd amodol ei bod wedi’i chynhyrchu ar beiriant A.

  2. Total Probability Rule 6 P(B) = P(B|A1)P(A1) + P(B|A2)P(A2) + ……+ P(B|Ar)P(Ar) • Example • Of the total daily output of a specific type of article at a factory, 40% are produced on machine A, 10% on machine B, and 50% on machine C. Of the articles produced on machine A, 60% are red and 40% are green. Of the articles produced on machine B, 30% are red and 70% are green. Of the articles produced on machine C, 50% are red and 50% are green. • Calculate the probability that an article chosen at random from a day’s total output will be green. • Given that the chosen article was green, calculate the conditional probability that it was produced on machine A.

  3. P(A) = 0.4 P(B) = 0.1 P(C) = 0.5 P(G|A) = 0.4 P(G|B) = 0.7 P(G|C) = 0.5 P(G) = P(G|A)P(A) + P(G|B)P(B) + P(G|C)P(C) P(G) = (0.4 x 0.4) + (0.7 x 0.1) + (0.5 x 0.5) P(G) = 0.16 + 0.07 + 0.25 P(G) = 0.48

  4. = P(G|A)P(A) P(G) b) P(A|G) = = 0.4 x 0.4 0.48 = 1 3 Ymarfer/Exercise 3.6 Mathemateg - Ystadegaeth Uned S1 – CBAC Mathematics Statistics Unit S1 - WJEC Ymarfer Ychwanegol Tebygolrwydd Cyflawn / Extra Questions on Total Probability Exercise Gwaith Cartref/Homework 5

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