During a tennis tournament, Tara and Emek studied the possible routes their teammate could take to the final. First, their teammate had a 0.8 probability of winning the quarterfinal. Meanwhile, another match would determine the semifinal opponent: Player A had a 0.6 probability of advancing, while Player B had a 0.4 probability. If their teammate reached the semifinal, past results suggested a 0.7 probability of defeating Player A but a 0.5 probability of defeating Player B. Tara organized the possibilities in a tree diagram. Emek multiplied probabilities along each route. The probability of reaching the final by facing Player A was 0.8 x 0.6 x 0.7 = 0.336, while the route through Player B had probability 0.8 x 0.4 x 0.5 = 0.160. Adding these paths gave an overall probability of 0.496, or 49.6%, of reaching the final. Since the route through Player A was more likely, they recommended spending more practice time preparing for that matchup while still reviewing tactics for Player B.




