Strategy Question (1 Viewer)

[Ignoratio Elenchi]

Then why is the number of possibilities relevant? Is it possible that the odds of the numerous possibilities you bring up that can happen if something goes wrong with the touchdown first strategy ending in a positive outcome are so small relative to the odds of the two strategies working perfectly to begin with that they don't have enough statistical relevance to make up for the disadvantage of going for the touchdown first as opposed to going for the field goal first?

See, this is a good example. That sentence is way too long. Take a deep breath. Figure out what you're trying to say. Break it up into little bullet points or something, if that helps. Make sure that what you're saying (a) makes sense, (b) addresses a point I actually made, instead of something you think I said, and © contributes towards the goal of figuring out the best game-winning strategy in this situation.Anyway, I should've just stuck with my commitment to stop responding. Good luck with whatever it is you do.

 

[Ignoratio Elenchi]

Is that the one when he thought RudiStein was a bail bondsman because of his Bad News Bears avatar?

I don't think I remember that one. golddigger never failed to entertain, though.

 

[shnikies]

Then why is the number of possibilities relevant? Is it possible that the odds of the numerous possibilities you bring up that can happen if something goes wrong with the touchdown first strategy ending in a positive outcome are so small relative to the odds of the two strategies working perfectly to begin with that they don't have enough statistical relevance to make up for the disadvantage of going for the touchdown first as opposed to going for the field goal first?

See, this is a good example. That sentence is way too long. Take a deep breath. Figure out what you're trying to say. Break it up into little bullet points or something, if that helps. Make sure that what you're saying (a) makes sense, (b) addresses a point I actually made, instead of something you think I said, and © contributes towards the goal of figuring out the best game-winning strategy in this situation.Anyway, I should've just stuck with my commitment to stop responding. Good luck with whatever it is you do.

Ha. Using your lack or reading comprehension as an excuse is funny. Thanks for admitting this is too complicated for you.

 

[SacramentoBob]

Is that the one when he thought RudiStein was a bail bondsman because of his Bad News Bears avatar?

I don't think I remember that one. golddigger never failed to entertain, though.

This is such . You show me a public school teacher that stated "Christianity is a myth" and didn't catch holy hell and I'll kiss your Jesus Fish emblem.

Do you have kids in public grade school to high school?

He's a public school teacher.

His icon is Chico's bail bond.

Are you saying that you are in fact a purple body of water?

It is a business icon- reasonable assumption he works there.

 

[SacramentoBob]

And now, back to our regularly scheduled fishing trip.

 

[shnikies]

This might help you and your fight against ADD:

Is it possible that "A" are so small relative to "B" that they don't have enough statistical relevance to make up for "C"?

A = the odds of the numerous possibilities you bring up that can happen if something goes wrong with the touchdown first strategy ending in a positive outcome

B = the odds of the two strategies working perfectly to begin with

C = the disadvantage of going for the touchdown first as opposed to going for the field goal first

 

[Ignoratio Elenchi]

I think these three are still unanswered:

[*]You're standing outside the nursery in the maternity ward of a hospital. You can't see in, but you know that there is exactly one boy and some unknown number of girls inside. Just then, a nurse walks into the nursery with another newborn, but you can't tell if it's a boy or a girl. A man, following close behind and grinning from ear to ear, points at the baby and exclaims, "Hi, I'm Bob, and that's my first child!" He then continues on down the hall sharing the good news with everyone he meets. A few minutes later, a baby is randomly selected from the nursery, and it is a boy. What is the probability that Bob's child is a girl?

[*]You have a bag containing 100 marbles, each of which is equally likely to be either white or black. At the time the bag was filled, every possible configuration of white and black (e.g. 50 whites/50 blacks, 100 whites/0 blacks, 73 whites/27 blacks) was equally likely. One at a time, you reach in and randomly select one, note its color, and return it to the bag. You do this 100 times and all 100 times you happen to pull a white marble. What is the probability that the bag contains 100 white marbles and no black marbles?

[*]An acquaintance offers to play a game where you bet on the outcome of a flipped coin. If it lands heads, you have to pay him a dollar; if it lands tails, he pays you $X. Sounds good, but you happen to know that he has two coins in his pocket, one of which is a normal fair coin and one of which is a trick coin with heads on both sides. You will play the game with one of these coins, but neither of you is sure which one (he will just randomly pull one out and start flipping).

2) If he pulls out one of the coins, flips it four times, and it comes up heads all four times, what is the probability that you're playing with the trick coin?

 

[Ignoratio Elenchi]

It is a business icon- reasonable assumption he works there.

 

[Ignoratio Elenchi]

Ha. Using your lack or reading comprehension as an excuse is funny.

I was using my reading comprehension, not my lack, fwiw.

 

[shnikies]

Ha. Using your lack or reading comprehension as an excuse is funny.

I was using my reading comprehension, not my lack, fwiw.

Thanks for pointing out my typo and not answering the question. Your maturity level is astonishing. Your mom must be proud.

 

[Instinctive]

I think these three are still unanswered:

[*]You have a bag containing 100 marbles, each of which is equally likely to be either white or black. At the time the bag was filled, every possible configuration of white and black (e.g. 50 whites/50 blacks, 100 whites/0 blacks, 73 whites/27 blacks) was equally likely. One at a time, you reach in and randomly select one, note its color, and return it to the bag. You do this 100 times and all 100 times you happen to pull a white marble. What is the probability that the bag contains 100 white marbles and no black marbles?

OK, on the marbles:You know it isn't 0 white and 100 black.

Shouldn't you calculate probability of getting all 100 white if # of White was anywhere from 1-99, and then add all of those together at some point? I'm going to be distracted my entire accounting class this afternoon now. I either get these problems immediately or I never do. That's what I get for not having to do math for 2 years though...

 

[Reepicheep]

I think these three are still unanswered:

[*]You have a bag containing 100 marbles, each of which is equally likely to be either white or black. At the time the bag was filled, every possible configuration of white and black (e.g. 50 whites/50 blacks, 100 whites/0 blacks, 73 whites/27 blacks) was equally likely. One at a time, you reach in and randomly select one, note its color, and return it to the bag. You do this 100 times and all 100 times you happen to pull a white marble. What is the probability that the bag contains 100 white marbles and no black marbles?

OK, on the marbles:You know it isn't 0 white and 100 black.

Shouldn't you calculate probability of getting all 100 white if # of White was anywhere from 1-99, and then add all of those together at some point? I'm going to be distracted my entire accounting class this afternoon now. I either get these problems immediately or I never do. That's what I get for not having to do math for 2 years though...

That's what I came up with. . . How often will 1 black/99 white result in 100 straight whites pulled? = x1 (i.e. .99^100=.366)

How about for 2 black/98 white? = x2

... etc

Chances all marbles are white = 1 / ( 1 + x1 + x2 + x3 ... + x99 )

I stopped at x7 when the values got real small and came up with .6357 (i.e. 64%)

I'm not certain this correct though.

 

[sn0mm1s]

I think these three are still unanswered:

[*]You have a bag containing 100 marbles, each of which is equally likely to be either white or black. At the time the bag was filled, every possible configuration of white and black (e.g. 50 whites/50 blacks, 100 whites/0 blacks, 73 whites/27 blacks) was equally likely. One at a time, you reach in and randomly select one, note its color, and return it to the bag. You do this 100 times and all 100 times you happen to pull a white marble. What is the probability that the bag contains 100 white marbles and no black marbles?

OK, on the marbles:You know it isn't 0 white and 100 black.

Shouldn't you calculate probability of getting all 100 white if # of White was anywhere from 1-99, and then add all of those together at some point? I'm going to be distracted my entire accounting class this afternoon now. I either get these problems immediately or I never do. That's what I get for not having to do math for 2 years though...

That's what I came up with. . . How often will 1 black/99 white result in 100 straight whites pulled? = x1 (i.e. .99^100=.366)

How about for 2 black/98 white? = x2

... etc

Chances all marbles are white = 1 / ( 1 + x1 + x2 + x3 ... + x99 )

I stopped at x7 when the values got real small and came up with .6357 (i.e. 64%)

I'm not certain this correct though.

On the marbles I got ~43%.For the trick coin I got 16/17

 

[Ignoratio Elenchi]

Chances all marbles are white = 1 / ( 1 + x1 + x2 + x3 ... + x99 )I stopped at x7 when the values got real small and came up with .6357 (i.e. 64%)

Correct (It's about 63.6%).

For the trick coin I got 16/17

Correct.

 

[Ignoratio Elenchi]

Last one yet to be solved:

You're standing outside the nursery in the maternity ward of a hospital. You can't see in, but you know that there is exactly one boy and some unknown number of girls inside. Just then, a nurse walks into the nursery with another newborn, but you can't tell if it's a boy or a girl. A man, following close behind and grinning from ear to ear, points at the baby and exclaims, "Hi, I'm Bob, and that's my first child!" He then continues on down the hall sharing the good news with everyone he meets. A few minutes later, a baby is randomly selected from the nursery, and it is a boy. What is the probability that Bob's child is a girl?

Here it is stripped of the "story":You have a certain (unknown) number of babies in a room, one of which is a boy, and the rest are girls. Then you add one more baby (whose gender is unknown). Then you randomly select one of the babies from the room, and it's a boy. What is the probability that the baby you added to the room was a girl?

 

[Ignoratio Elenchi]

The parameters are described in a slightly confusing way; it sounds like by the first clause that there are 50 white and 50 black marbles in the bag, in which case the answer would be zero probability that it contains 100 white marbles. If you mean that there was a 50% chance for each marble to be white or black, the probability is .5^100; the number of white marbles pulled out is irrelevant.

The way I stated it was yes, there was initially a 50% chance for each marble to be white or black (I'm recalling this problem from memory, and think that's actually a mistake). The correct interpretation, IIRC, is that any combination of marbles in the bag is equally likely. We don't actually know how many of each are in the bag. It's possible that there are exactly 50 of each, or maybe there are 40 white and 60 black, or maybe there are 100 white and 0 black. Each of these scenarios is equally likely to be what's actually in the bag.Either way I think your answer is incorrect. But let's scrap this one for a bit so I can work it out and correctly state the problem.

So I didn't intend to word the problem as I originally did ("each marble is equally likely to be white or black"), but that does make for kind of an interesting question. I think I have it worked out so I'll leave it out there if you want to take a stab at it. It's not .5100 - if every marble was equally likely to be white or black, it would be very unlikely that you would happen to fill the bag with 100 white marbles and zero black marbles. It would be much more likely that you'd end up with somewhere around 50 white and 50 black.But then, once we've filled the bag and you start pulling white marble after white marble, it becomes more and more likely that the bag actually is predominantly filled with white marbles, despite how unlikely that might have been at the outset.

So you have two competing probablilites - the unlikely probability that you would fill the bag with all white marbles in the first place, and then the unlikely probability that the bag isn't filled with all white marbles if you keep pulling white ones out without ever pulling a black one. I'll leave it to the interested reader (shnikies?) to figure out which probability outweighs the other and what the answer would be if the question were worded this way.

Maybe another interesting question would be: How many times would you have to pull out a white marble (without ever pulling a black marble) to be, say, 99% sure that there were no black marbles in the bag?

Perhaps to make it simpler, consider a bag with three marbles. Each one is equally likely to be white or black when the bag is filled. Then one at a time and with replacement, you pull out a marble and note its color. How many times would you have to pull out a white marble (without ever pulling a black marble) to be 99% sure that there were actually no black marbles in the bag?

 

[shnikies]

Bump

Just looking for the people who think Lovie Smith knows better than Bill Belichick.

 

[CalBear]

BumpJust looking for the people who think Lovie Smith knows better than Bill Belichick.

I think I found the people who can't count to 11 without taking off their shoes.

 

[Ignoratio Elenchi]

9-11 is a poor range. Being down by 9 or 10 is completely different from being down by 11. The 2 point conversion being necessary changes the equation.

 

[Ignoratio Elenchi]

BumpJust looking for the people who think Lovie Smith knows better than Bill Belichick.

Lovie Smith was down by 11. Bill Belichick was down by 10. You don't believe that's a relevant difference?