In a tournament, a team plays 10 matches with probabilities of winning and losing each match as 1 3 and 2 3 respectively. Let x be the number of matches that the team wins, and y be the number of matches that team loses. If the probability P (|x-y| 2) is p , then 3^9 p equals ______

Step-by-step solution

aligned & P(W)= 1 3 P(L)= 2 3 & x= number of matches that team wins & y= number of matches that team loses & |x-y| 2 and x+y=10 & |x-y|=0,1,2 x, y N aligned Case-I aligned & -I:|x-y|=0 x=y & x+y=10 x=5=y & P(|x-y|=0)= ¹⁰ C₅ ( 1 3 )^5 ( 2 3 )^5 aligned Case-II : | x - y |=1 x - y = 1 array |c|c| x = y +1 & x = y -1 x + y =10 & x + y =10 2 y =9 & 2 y =11 Not possible & Not possible array aligned & Case-III : | x - y |=2 x - y = 2 & x-y=2 OR x-y=-2 & x + y =10 x + y =10 & x=6, y=4 x=4, y=6 & P (| x - y |=2)= ¹⁰ C ₆ (