Math Probability Question?

Liz and Josh are heated competitors in a video game. Each has a 50% chance of victory in the first round, but Liz is very emotional. When Liz wins, he

Liz and Josh are heated competitors in a video game. Each has a 50% chance of victory in the first round, but Liz is very emotional. When Liz wins, her chance of victory in the next round increases to 70%. When she loses, her chance of victory in the next round decreases to 20%. What is the probability of Liz's winning at least two out of three games?

or:Liz and Josh are heated competitors in a video game. Each has a 50% chance of victory in the first round, but Liz is very emotional. When Liz wins, her chance of victory in the next round increases to 70%. When she loses, her chance of victory in the next round decreases to 20%. What is the probability of Liz's winning at least two out of three games?

or:The result of a game determines the probabiity P to win/lose the next game, i.e. P is established before the game in which it takes effect is started. Thus P0 goes into Game 1, P1 in game 2 and so forth.Game 1:P0 = 0.5IF Liz wins, THEN P1 = 0.7IF Liz loses, THEN P1 = 0.2Game 2:P1 = 0.7IF Liz wins, THEN P2 = 0.7IF Liz loses, THEN P2 = 0.2P1 = 0.2IF Liz wins, THEN P2 = 0.7IF Liz loses, THEN P2 = 0.2Game 3:P2 = 0.7P2 = 0.2 ....Liz has 3 ways to win 2 games out of three:1) she wins the 1st and the 2nd (wins game and set: no 3rd game required)2) she wins 1st and 3rd (loses 2nd)3) she wins 2nd and 3rd (loses 1st)The probabiity for winning the 1st game is always 0.5 (50%)So, the chances for Liz to win a set of two games out of three are:1) 0.5 * 0.7 = 0.35+2) 0.5 * 0.7 * 0.2 = 0.07+3) 0.5 * 0.2 * 0.7 = 0.07=0.35 + 0.07 + 0.07 = 0.49Liz's chances to win this set are 49%.

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