Ann, Bob, Carl, and Dan are randomly lined up. The first two players in line then play a game; the winner of that game plays a game with the person who is third in line; the winner of that game then plays a game with the person who is fourth in line. The winner of that last game gets a big prize. Suppose Ann wins each game with probability 0.8, regardless who she is playing against. Find the probability that Ann is the one to win the big prize

The probability of Ann winning the prize is 2.464

Explanation:

The probability of Ann winning the prize can be analysed as potray below

1.pr(of Ann being the first player selected).

Here Ann plays the 2nd,3rd and 4th player to win prize,the probability=0.8×0.8×0.8=0.512

2.Pr(of Ann being the second player selected)

If Ann is randomly selected as the second player,she will still need to play three matches to win with 1st,3rd and 4th

0.8×0.8×0.8=0.512

3.Pr(of Ann. Being the third player chooses randomly),Ann will get to play just two players i.e the winner of 1and 2 and the 4th.the probability=0.8×0.8=0.64

4.Pr(of Ann being the 4th player choosen randomly)

Ann gets to play only one match to win the prize in this scenario

So probability of a Ann win is 0.8

Total probability a Ann winning the prize=0.512+0.512+0.64+0.8=2.464

i believe that it is a 45% chance.