### Brain Teasers

# Tipping

Probability
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

There are 14 teams in the National Rugby League. During Round 6, every team plays another team, so there are 7 matches. What is the probability of Glenn tipping every match right?

### Answer

0.0457%Presuming all three possible outcomes of each match (i.e. win, lose or draw) are equally likely, then there is a 1 in 3 chance of predicting each match. With 7 matches, the probability becomes 1 in 2187 or 0.0457%.

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## Comments

i am ignorat about rugby. please exlpane.

The question wouldn't chnage if it was basketball or soccer, etc.

but what is tipping a match? i think something is lost in the translation...

I'm assuming that "tipping" means that he picked the winner in each match. If so, then 1) This is invalid because you need to take into consideration Glenn's knowledge of the game. Does he know who the favored team is in each game? If so, his odds will go up. 2) If this teaser were the equivalent of correctly guessing 7 coin tosses (which it isn't), wouldn't the probability be 1 in 2^7 or 1/128? Where did the 4.75% come from?

presuming all three possible outcomes of each match (i.e. win, lose or draw) are equally likely, then there is a 1 in 3 chance of pridicting each match. With 7 matches the probability becomes 1 in 2187 or 0.0457%. Your . is in the wrong place!

then the answer should be 0.0457% and not 4.57%

OK - I forgot about ties. However, even if you move the decimal point, Glennboy's answer still isn't .0457, it's .0475. Glennboy...How did YOU get your answer? ...and I still say that this teaser is invalid. For example, if the British national team played a junior high school team do you really think Glenn's odds of picking the outcome would be 1 in 3?

OK, Bobbrt I think you haven't thought through your example very well. The thing that Glenn was picking was clearly stated to be 'THE NATIONAL RUGBY LEAGUE' where the top teams play each other, not where national teams play high school teams. Now, the draw would be non-existant as for extra time! Glenn only picks once so he has odds of 1/21 which is equivilent to 21 which is approximately equal to 4.75%!

Now you're REALLY off. So you say there are no ties. Fine. WHERE does the 1 in 21 come from? If there are no ties, then the probability is 1/2^7, which is 1 in 128. PLUS, my point about the high school team was to show that if Glenn knows anything about the rugby teams, then the odds change: If the top seed plays the bottom seed, Glen should pick the top seed, and would have a better chance of winning. This teaser is NOT like a 50-50 coin flip. Each team's odds of winning is NOT 50-50.

Ok, technically i was wrong...but mathematically i waan't

Then explain the 1 in 21. Where does it come from? You say that your math is correct, but no one else has gotten the same answer as you. Just explain your answer in detail.

break it up Glen and Bob!

........huh............?

Unfortunately, probability is a very easy topic to get numbers twisted in. The odds of tipping one game are 1 in 3, or 1/3=.3333333 . The odds of tipping two games are

(1/3)(1/3)=.1111111 . So now you can see how the odds of tipping all correctly would be (1/3)^7=.0457247% It is very easy to assume that it would be 1/21=4.7619048% but this is incorrect. This incorrect number could be obtained from (1/3)*(1/7), odds of one game times odds of all games, which is obviously incorrect.

(1/3)(1/3)=.1111111 . So now you can see how the odds of tipping all correctly would be (1/3)^7=.0457247% It is very easy to assume that it would be 1/21=4.7619048% but this is incorrect. This incorrect number could be obtained from (1/3)*(1/7), odds of one game times odds of all games, which is obviously incorrect.

Anybody out there who wants to get brain damage to the probability part of their thinking apparatus? Does anybody know that probability deals with equally likely outcomes? Win lose and draw are not equally likely. Even if I was tipping the underwater 3 legged camel polo and flipped a three sided coin to decide my tip, it still wouldn't have anything to do with who actually wins! That surely has got to do with which camel has got the humps and who payed the jockeys. There is no way you can calculate a probability of any kind that remotely adresses the question asked in this teaser!

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