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jackie and phil have two fair coins and a third coin that comes up heads with probability 4/7 . jackie flips the three coins, and then phil flips the three coins. let m/n be the probability that jackie gets the same number of heads as phil, where m and n are relatively prime positive integers. find m +n

Answer :

Here m/n be the probability of  123/392, where m is  123 and n is 392,  so the  m+n is  515  

Here considering xⁿ to be the flipping heads of n numbers , so the generating functions for these coins are (1+x)(1+x)(3+4x) order, so  the  product those orders we get ,

(1+x)*(1+x)*(3+4x)= 4x^3+11^2+10x+3 ,here axⁿ means the n number of ways to get n number of  head .Now the square of the sum of the coefficient is (4+11+10+3)²= 28^2 =784, and the sum of the square of each coefficient is(4²+11²+10²+3²)=  246.The probability will be: 246/784=123/392 =123+392 =  515  

To know more about probability refer to the link  brainly.com/question/27430404

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