Alex and julia are playing in a tennis tournament. They will play each other twice and each has an equal chance of winning the first game. If Alex wins the first game his confidence increases, and his probability of winning the second game is increased to 0.55. If he loses the first game he loses heart so that the probability of of winning the second game is reduced to 0.25. find the probability that alex wins one game.

Question

anonymous · Answer

it is 7/50 -if he has to win only one game.
it is 1/4 i if he has to win atleast one game

anonymous · Answer

there are two ways for him to win exactly 1 game.  a win follow by a loss or a loss followed by a win.  the probability of win loss is .5 (win)*.45 (loss)= .225 (22.5%).  the probability of a loss followed by a win is .5 (loss) *.25 (win) =.125 (12.5%) adding these together you get a total of .35 or 35%

anonymous · Answer

can win win be included aswell?

anonymous · Answer

jsut add .5*.55 (win win)=.275, bringing the total to .625 or 62.5%

anonymous · Answer

if win win is included as well, the easiest way to calculate this is to subtract (loss loss), .5*.75=.375, from 1, so 1-.375=.625, same answer

anonymous · Answer

sorry the previuos ans is wrong i did calc mistake
it is 7/20 -if he has to win only one game. 
it is 5/8 i if he has to win atleast one game

anonymous · Answer

k thanks everyone:)