Question: To calculate (1)P(A1B) using Bayes' theorem, we will plug the given probabilities into the formula: (1)=(1)(1)(1)(1)+(2)(2)P(A1B)=P(A1)P(BA1)+P(A2)P(BA2)P(A1)P(BA1) Given: (1)=5/365=0.0136985P(A1)=5/365=0.0136985 (2)=360/365=0.9863014P(A2)=360/365=0.9863014 (1)=0.9P(BA1)=0.9 (2)=0.1P(BA2)=0.1 Let us calculate: (1)=(0.0136985)(0.9)(0.0136985)(0.9)+(0.9863014)(0.1)P(A1B)=(0.0136985)(0.9)+(0.9863014)(0.1)(0.0136985)(0.9)

To calculate (1)P(A1B) using Bayes' theorem, we will plug the given probabilities into the formula: (1)=(1)(1)(1)(1)+(2)(2)P(A1B)=P(A1)P(BA1)+P(A2)P(BA2)P(A1)P(BA1) Given: (1)=5/365=0.0136985P(A1)=5/365=0.0136985 (2)=360/365=0.9863014P(A2)=360/365=0.9863014 (1)=0.9P(BA1)=0.9 (2)=0.1P(BA2)=0.1 Let us calculate: (1)=(0.0136985)(0.9)(0.0136985)(0.9)+(0.9863014)(0.1)P(A1B)=(0.0136985)(0.9)+(0.9863014)(0.1)(0.0136985)(0.9) (1)=0.012328650.01232865+0.09863014P(A1B)=0.01232865+0.098630140.01232865 (1)=0.012328650.11095879P(A1B)=0.110958790.01232865 (1)0.11111P(A1B)0.11111

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