Teaching an intelligent guy about a basic statistics concept

[soon2bepro]

A friend of mine who has a decent understanding of statistics believes that since random results will average out in the long run, when there's a variation from the standard, it will tend to go the other way in the future.

For example, he believes that if you flip a coin 10 times and get 10 heads, you're slightly more likely to get a tails next time since 11 heads in a row is very unlikely.

This is an intelligent guy, but I can't get to him on this. I'm not a good teacher.

What approach do you reccomend?

I've tried the "you're adjudicating a mystical power to the coin", the "the past doesn't influence the future in this way", and the "new information about the way things went affects how you project the long term result, so you can't expect to go 100 heads and 100 tails on average for 200 flips after you've gotten 10 heads in a row"; but none of these seem to work.

[tshort]

Your friend is not intelligent.

Edit: So, you take a fair coin and 10 flips in a row are heads. He now can have one of three assumptions:

1) Heads is more likely on the next flip
2) Tails is more likely on the next flip
3) They are equally likely

Ask him why he doesn't think heads is more likely?

[Justin A]

Offer to bet him. Say you'll repeatedly. flip a coin, and every time it comes up five in a row heads or tails, you will bet on the same result for the sixth toss, as long as he gives you 11:10.

At least if you can't convince him you'll make some money.

[Silent A]

Intelligent people can believe pretty silly things (like the medical doctor I met who insisted that Martingale betting was risk free easy money). The problem is that they tend to have too much of an ego about such things to admit that they're wrong about something so simple.

Some ideas though:
1) ask him to calculate the odds of a fair coin coming up heads once
2) ask him to calculate the odds of it coming up heads twice
3) ask him to calculate the odds of it coming up heads 10 times in a row
4) ask him to calculate the odds of it coming up heads one more time after it has come up heads 10 times in a row
5) ask him to calculate the odds of it coming up heads 11 times in a row

Now see if he applies probability theory consistently as he does this.

[Phil153]

Bring it down to simple physics, and ask him if the movement of your fingers or the air currents in the room are going to change depending on whether the last throw was heads or tails.

[yukoncpa]

The law of probability doesn’t say random results will even out in the long run. The more coin flips that you have, the more likely you will APPROACH the true odds.

Example: if the first 10 flips are heads and every other flip is tails, heads, tails, etc, then after 100 flips, you will have 55/45 or heads will come up 55 percent. After 1000 flips you will have 505/495 or heads will come up 50.5 percent of the time. The more flips you have the closer the odds of heads coming up will be 50% even though, at all times, the first 10 flips were heads.

[vhawk01]

This seems like a really easy problem. Just ask him if he thinks anyone ever flipped that coin before the cashier at the supermarket gave it to him.

[soon2bepro]

[ QUOTE ]
Example: if the first 10 flips are heads and every other flip is tails, heads, tails, etc, then after 100 flips, you will have 55/45 or heads will come up 55 percent. After 1000 flips you will have 505/495 or heads will come up 50.5 percent of the time. The more flips you have the closer the odds of heads coming up will be 50% even though, at all times, the first 10 flips were heads.

[/ QUOTE ]

I'm gonna try this one and let you guys know. It seems like it will work.

Thanks for the help.

[Nicholasp27]

[ QUOTE ]
A friend of mine who has a decent understanding of statistics believes that since random results will average out in the long run, when there's a variation from the standard, it will tend to go the other way in the future.

[/ QUOTE ]

it doesn't have to go the other way in the future...imagine it goes 100 tails in a row to start...now it's 100% tails and 0% heads...he's thinking that there should now be 100 more heads than tails over the next 'long run' set of flips to 'even it out'

that's incorrect


what if it now goes 10mil heads to 10mil tails? that 100 no longer is significant...10mil heads to 10mil+100 tails is still 50/50 (49.99975% heads)...get it to billions etc and it's even closer

so no, it doesn't have to 'even out'...

and no matter how u look at it, there is no memory, so it's always 50/50 in any individual coinflip

[Follow]

[ QUOTE ]
[ QUOTE ]
A friend of mine who has a decent understanding of statistics believes that since random results will average out in the long run, when there's a variation from the standard, it will tend to go the other way in the future.

[/ QUOTE ]

it doesn't have to go the other way in the future...imagine it goes 100 tails in a row to start...now it's 100% tails and 0% heads...he's thinking that there should now be 100 more heads than tails over the next 'long run' set of flips to 'even it out'

that's incorrect


what if it now goes 10mil heads to 10mil tails? that 100 no longer is significant...10mil heads to 10mil+100 tails is still 50/50 (49.99975% heads)...get it to billions etc and it's even closer

so no, it doesn't have to 'even out'...

and no matter how u look at it, there is no memory, so it's always 50/50 in any individual coinflip

[/ QUOTE ]

I like this explanation. It works well for the Monty Hall riddle too.




Follow [img]/images/graemlins/smile.gif[/img]