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# In order to make the national tennis team, Matt

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In order to make the national tennis team, Matt  [#permalink]

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23 Jun 2014, 21:02
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Difficulty:

95% (hard)

Question Stats:

35% (02:18) correct 65% (02:22) wrong based on 382 sessions

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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%.

Love this question. Kindly provide your explanations.
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Re: In order to make the national tennis team, Matt  [#permalink]

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14 Aug 2014, 02:14
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jogeshanand 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%.

Love this question. Kindly provide your explanations.

Consider this:

Matt has to beat Steve as well as Larry. Taking only statement 2, the probability that Matt beats Larry is 30%. But he actually has to beat Steve too. What is the best probability of Matt going through? It is if he will beat Steve for sure i.e. probability of beating Steve is 1.

So assuming he plays Steve-Larry-Steve, his probability of going through is 1*(3/10)*1 = 3/10

Assuming he plays Larry-Steve-Larry, his probability of going through is (3/10)*1*1 + (7/10)*1*(3/10) = 51/100
(3/10)*1*1 -> Wins first two games and whatever happens to third, doesn't matter
(7/10)*1*(3/10) -> Loses the first game but wins other two

Hence, statement 2 is sufficient to say that "No, his probability of making the team is not greater than 51%."
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Re: In order to make the national tennis team, Matt  [#permalink]

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14 Aug 2014, 01:13
Let's assume p(steve) = s and p(lorry) = l

for S-L-S p(win) = s^2 + 2sl
for L-S-L p(win) = l^2 + 2sl

how could l alone help us know the answer ? Please explain. I think answer is E
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Re: In order to make the national tennis team, Matt  [#permalink]

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03 Jan 2015, 01:17
VeritasPrepKarishma wrote:
jogeshanand 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%.

Love this question. Kindly provide your explanations.

Consider this:

Matt has to beat Steve as well as Larry. Taking only statement 2, the probability that Matt beats Larry is 30%. But he actually has to beat Steve too. What is the best probability of Matt going through? It is if he will beat Steve for sure i.e. probability of beating Steve is 1.

So assuming he plays Steve-Larry-Steve, his probability of going through is 1*(3/10)*1 = 3/10

Assuming he plays Larry-Steve-Larry, his probability of going through is (3/10)*1*1 + (7/10)*1*(3/10) = 51/100
(3/10)*1*1 -> Wins first two games and whatever happens to third, doesn't matter
(7/10)*1*(3/10) -> Loses the first game but wins other two

Hence, statement 2 is sufficient to say that "No, his probability of making the team is not greater than 51%."

So assuming he plays Steve-Larry-Steve, his probability of going through is 1*(3/10)*1 = 3/10 --> shouldn't it be 1*(3/10)*1 + (7/10)*1*(3/10) = still 51/100 , just want to make sure it was missed and not that i am doing something wrong.
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Re: In order to make the national tennis team, Matt  [#permalink]

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04 Jan 2015, 21:20
Lucky2783 wrote:

So assuming he plays Steve-Larry-Steve, his probability of going through is 1*(3/10)*1 = 3/10 --> shouldn't it be 1*(3/10)*1 + (7/10)*1*(3/10) = still 51/100 , just want to make sure it was missed and not that i am doing something wrong.

No. Assuming he plays Steve-Larry-Steve, his probability of going through is only 1*(3/10)*1 = 3/10
He must win two games in a row. That means he must win the game with Larry in any case.
Taking the best case scenario i.e. the case in which he will definitely roll over Steve i.e. his probability of winning over Steve is 1,
we get 1*(3/10)*1 (Win-Win-Win) - the only way in which he goes through if he plays Steve-Larry-Steve.

Think what happens if the probability of winning from Steve is less than 1, say 9/10.

His probability of going through will be (9/10)*(3/10) (Win-Win) + (1/10)*(3/10)*(9/10) (Lose-Win-Win)
= 270/1000 + 27/1000 = 297/1000 (less than 3/10)
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Re: In order to make the national tennis team, Matt  [#permalink]

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20 Sep 2016, 05:58
jogeshanand 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%.

Love this question. Kindly provide your explanations.

Statement 1. - clearly not sufficient
Statement 2. - probability- Matt beats Larry = 3/10, lets says his chance of beating steve is 99%, i.e, 99/100, then
L-S-L = 3/10 x 99/100 x 3/10 = 891/10000 = no way, he cant make it -
S-L-S = 99/100 x 3/10 X 99/100 = 29403/100000 = oh no... ... sorry matt, try next year bro
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In order to make the national tennis team, Matt  [#permalink]

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08 Feb 2017, 04:30
VeritasPrepKarishma wrote:
jogeshanand 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%.

Love this question. Kindly provide your explanations.

Consider this:

Matt has to beat Steve as well as Larry. Taking only statement 2, the probability that Matt beats Larry is 30%. But he actually has to beat Steve too. What is the best probability of Matt going through? It is if he will beat Steve for sure i.e. probability of beating Steve is 1.

So assuming he plays Steve-Larry-Steve, his probability of going through is 1*(3/10)*1 = 3/10

Assuming he plays Larry-Steve-Larry, his probability of going through is (3/10)*1*1 + (7/10)*1*(3/10) = 51/100
(3/10)*1*1 -> Wins first two games and whatever happens to third, doesn't matter
(7/10)*1*(3/10) -> Loses the first game but wins other two

Hence, statement 2 is sufficient to say that "No, his probability of making the team is not greater than 51%."

Dear VeritasPrepKarishma, What is the methodology used to calculate the yellow highlight? I have no idea how you get there? Why whatever happens to third doesn't matter?

Matt beat Larry = 30%=0.3
Matt beat Steve = ?
Larry-Steve-Larry
(Win)(Win)(Lose)?
(Win)(Win)(Win)?
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Re: In order to make the national tennis team, Matt  [#permalink]

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08 Feb 2017, 21:49
1
ziyuenlau wrote:
Dear VeritasPrepKarishma, What is the methodology used to calculate the yellow highlight? I have no idea how you get there? Why whatever happens to third doesn't matter?

Matt beat Larry = 30%=0.3
Matt beat Steve = ?
Larry-Steve-Larry
(Win)(Win)(Lose)?
(Win)(Win)(Win)?

There are only two ways in which Matt can play the games:

Larry-Steve-Larry
Steve-Larry-Steve

According to data given in stmnt 2, we know that the probability that Matt beats Larry is 30%. We would like to find the maximum probability that Matt goes through to see if it is more than 51%. So in the best case scenario, Matt beats Steve with a probability of 1 i.e. definitely beats Steve. This will give us the maximum probability of Matt going through. If we find that it is not more than 51%, then we can be sure that whatever the actual probability of Matt beating Steve, the probability of Matt going through cannot be more than 51%.

If he plays Steve-Larry-Steve, his probability of going through is 1*(3/10)*1 = 3/10
He will win the first and third games and to go through, he must win the second one too since he needs to win two consecutive games (given in the question). So just winning 1st and 3rd are not enough.

If he plays Larry-Steve-Larry, his probability of going through is (3/10)*1*1 + (7/10)*1*(3/10) = 51/100
How do we get this? To win two consecutive games, he could win the first and second games or second and third games.
(3/10)*1*1 -> Wins first two games and goes through. Then the outcome of the third game is immaterial. Whether he wins or loses, he will still go through.
(7/10)*1*(3/10) -> Loses the first game with the probability of 7/10 since he plays it against Larry, but wins the other two games - one against Steve and the other against Larry.
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In order to make the national tennis team, Matt  [#permalink]

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08 Feb 2017, 21:58
VeritasPrepKarishma wrote:

If he plays Steve-Larry-Steve, his probability of going through is 1*(3/10)*1 = 3/10
He will win the first and third games and to go through, he must win the second one too since he needs to win two consecutive games (given in the question). So just winning 1st and 3rd are not enough.

If he plays Larry-Steve-Larry, his probability of going through is (3/10)*1*1 + (7/10)*1*(3/10) = 51/100
How do we get this? To win two consecutive games, he could win the first and second games or second and third games.
(3/10)*1*1 -> Wins first two games and goes through. Then the outcome of the third game is immaterial. Whether he wins or loses, he will still go through.
(7/10)*1*(3/10) -> Loses the first game with the probability of 7/10 since he plays it against Larry, but wins the other two games - one against Steve and the other against Larry.

Dear VeritasPrepKarishma, What if Matt loses to Larry on the third game, the probability will become (3/10)*1*(7/10)? Then, your probability in blue font still valid since you assuming that he wins the third game.
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Re: In order to make the national tennis team, Matt  [#permalink]

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09 Feb 2017, 00:59
2
ziyuenlau wrote:
VeritasPrepKarishma wrote:

If he plays Steve-Larry-Steve, his probability of going through is 1*(3/10)*1 = 3/10
He will win the first and third games and to go through, he must win the second one too since he needs to win two consecutive games (given in the question). So just winning 1st and 3rd are not enough.

If he plays Larry-Steve-Larry, his probability of going through is (3/10)*1*1 + (7/10)*1*(3/10) = 51/100
How do we get this? To win two consecutive games, he could win the first and second games or second and third games.
(3/10)*1*1 -> Wins first two games and goes through. Then the outcome of the third game is immaterial. Whether he wins or loses, he will still go through.
(7/10)*1*(3/10) -> Loses the first game with the probability of 7/10 since he plays it against Larry, but wins the other two games - one against Steve and the other against Larry.

Dear VeritasPrepKarishma, What if Matt loses to Larry on the third game, the probability will become (3/10)*1*(7/10)? Then, your probability in blue font still valid since you assuming that he wins the third game.

When I say the probability is (3/10)*1*1, it includes both Matt winning from Larry and Matt losing to Larry in the third game.

Winning + Losing
(3/10)*1*(3/10) + (3/10)*1*(7/10)
= (3/10)*1*(3/10 + 7/10)
= (3/10)*1*1

Basically, it doesn't matter what happens in the third game.
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Re: In order to make the national tennis team, Matt  [#permalink]

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26 Mar 2017, 03:52
VeritasPrepKarishma

Do I always have the liberty to choose probability of 1 when Matt beats Steve??

I actually consider 40% & 50% probability of beating Steve (they both are better than 30%) and got two different result.Hence got the answer choic E.
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Re: In order to make the national tennis team, Matt  [#permalink]

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27 Mar 2017, 02:57
1
techiesam wrote:
VeritasPrepKarishma

Do I always have the liberty to choose probability of 1 when Matt beats Steve??

I actually consider 40% & 50% probability of beating Steve (they both are better than 30%) and got two different result.Hence got the answer choic E.

No, not at all. The probability of Matt beating Steve could very well be 40%, 50%, 67%, or 100% (i.e. 1) etc.

But in this question we need to find if the probability of Matt winning is more than 51%. So let's try to find out the BEST POSSIBLE case for Matt. If that probability is more than 51%, then we know that we do not enough information to answer the question.

Say, we assume that probability of Matt beating Steve is 40%. Say, in that case, we get that probability of Matt making the team is 10% (just assumption).

Say, we assume that probability of Matt beating Steve is 50%. Say, in that case, we get that probability of Matt making the team is 15% (just assumption).

Say, we assume that probability of Matt beating Steve is 80%. Say, in that case, we get that probability of Matt making the team is 35% (just assumption).

Say, we assume that probability of Matt beating Steve is 100%. In that case, we get that probability of Matt making the team is 51% (we have calculated above).

Now, we see that 51% is the highest possible probability of Matt making the team. So can the probability of Matt making the team be more than 51%? No.

If, instead, at 100%, we would have got that the probability of Matt making the team is, say 55%, then we would have been unable to say whether the probability of Matt making the team is more than 51% or not. The answer would depend on the actual probability of Matt beating Steve.

But in our original question, no matter what the probability of Matt beating Steve, the probability of Matt making the team will NEVER be more than 51%.
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Re: In order to make the national tennis team, Matt  [#permalink]

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