In order to make the national tennis team, Matt has to play a three-game series against Larry and Steve, and in doing so win two games in a row. He's given a choice, however: he can choose the order in which he plays against his opponents but cannot play the same opponent in consecutive games (so he could play Larry-Steve-Larry OR Steve-Larry-Steve). Assuming that Matt chooses the three-game sequence that maximizes his probability of making the national team, is his probability of making the team greater than 51%?
(1) Matt's probability of beating Steve are better than Matt's probability of beating Larry
(2) The probability that Matt beats Larry is 30%
OA : B
Source : Veritas Prep
Tennis Team
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Question : Is his probability of making the team greater than 51%?manik11 wrote:In order to make the national tennis team, Matt has to play a three-game series against Larry and Steve, and in doing so win two games in a row. He's given a choice, however: he can choose the order in which he plays against his opponents but cannot play the same opponent in consecutive games (so he could play Larry-Steve-Larry OR Steve-Larry-Steve). Assuming that Matt chooses the three-game sequence that maximizes his probability of making the national team, is his probability of making the team greater than 51%?
(1) Matt's probability of beating Steve are better than Matt's probability of beating Larry
(2) The probability that Matt beats Larry is 30%
OA : B
Source : Veritas Prep
Statement 1: Matt's probability of beating Steve are better than Matt's probability of beating Larry
No Values of Probabilities are given for calculation of Matt's winning 2 games in row hence,
NOT SUFFICIENT
Statement 2: The probability that Matt beats Larry is 30%
To win two games in sequence, matt has to play one game with Steve and One with Larry
even if the probability of matt winning game against Steve =1
then Maximum Probability of Matt winning two games in sequence = 0.3*1 = 0.3
i.e. in best possible scenario as well Matt will not be able to make his team.
SUFFICIENT
Answer: Option B
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For statement 1, you can try some extreme scenarios. Say Matt's probability of beating Steve is 100% and his probability of beating Larry is 99%. No need to do any math here- clearly his probability of winning two in a row is over 51%. So that's a YES. Now say Matt's probability of beating Steve is 1% and his probability of beating Larry is .5%. Clearly, his probability of winning two in a row is not over 51%, so that's a NO. Statement 1 is not sufficient.manik11 wrote:In order to make the national tennis team, Matt has to play a three-game series against Larry and Steve, and in doing so win two games in a row. He's given a choice, however: he can choose the order in which he plays against his opponents but cannot play the same opponent in consecutive games (so he could play Larry-Steve-Larry OR Steve-Larry-Steve). Assuming that Matt chooses the three-game sequence that maximizes his probability of making the national team, is his probability of making the team greater than 51%?
(1) Matt's probability of beating Steve are better than Matt's probability of beating Larry
(2) The probability that Matt beats Larry is 30%
OA : B
Source : Veritas Prep
Statement 2 is more complex than it appears at first glance. First, if Matt has to alternate between Larry and Steve, he'll need to beat both players in order to win two in a row. We know that Matt has a 30% probability of beating Larry. (And a 70% chance of losing to Larry.) Obviously the highest possible probability that Matt will beat Steve is 100%. So let's examine that scenario.
Now he has a choice. He can play Larry-Steve-Larry or he can play Steve-Larry-Steve. It may feel counterintuitive, but Matt's odds of winning two straight are better with the first scenario. (Think of it this way: he has to beat Larry in order to win two in a row. In the first scenario, he gets two cracks at Larry. In the second one, he only gets one.)
So then what is the probability that Matt wins at least two in a row, if he plays Larry-Steve-Larry? Well, we know he beats Steve, if there's a 100% probability of victory. So as long as Matt beats Larry at least once, he'll win two in a row. (He could win the first two or the last two or all three.)
P(beat Larry at least once) = 1 - P(never beat Larry)
P(never beat Larry) = .7 *.7 = .49
1 - P(never beat Larry) = 1 - .49 = .51. Meaning the best possible scenario entails a 51% chance that Matt wins at least two in a row. Therefore, we know that the probability is never higher than 51%, and thus statement 2 alone is sufficient. Tricky question.
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... and the Matt in this problem is me! (Steve would have to be REALLY terrible for me to have a 90%+ chance of beating him, I can barely get the ball over the net.)
The spirit of this Q, by the way, is to test your GMAT instincts: S1 alone is obviously NOT sufficient, and the two TOGETHER is a little too easy, so you want to be pick S2 alone even if you can't entirely reason it out in two minutes.
The spirit of this Q, by the way, is to test your GMAT instincts: S1 alone is obviously NOT sufficient, and the two TOGETHER is a little too easy, so you want to be pick S2 alone even if you can't entirely reason it out in two minutes.