Question

Studies indicate that the probability that a married man votes is 0.45, the probability that a married woman votes is 0.40, and the probability that a married woman votes given that her husband does is 0.60. Compute the following probabilities:
(a) Both a man and his wife vote.
(b) A man votes given that his wife does.

Answer 1

    Define following events                  
   A: married man votes                  
   B: married woman votes                  
   Given                  
   P(A) = 0.45                  
   P(B) = 0.4                  
   P(B | A) = 0.6                  

                      
1)   To find P(both a man and his wife vote)                  
   that is to find P(A AND B)                  
   By Baye's conditional probability theorem                  
   P(B | A) = P(A AND B) / P(A)                  
   P(A AND B) = P(B | A) * P(A)                  
       = 0.6 * 0.45              
       = 0.27              
   P(both a man and his wife vote) = 0.27                 
                      
2)   To find P(a man votes given that his wife votes)                  
   that is to find P(A | B)                  
   By Baye's conditional probability theorem                  
   P(A | B) = P(A AND B) / P(B)                  
       = 0.27 / 0.4       (from 1, P(A AND B) = 0.27)      
       = 0.675              
   P(a man votes given that his wife votes) = 0.675                  

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