to ask if you can answer a question re probability (Maths question)

[Fainne]

So, say I have 20 cards in a pack.

I pick one. It's the Ace of Diamonds let's say for argument's sake.

I then pick another one out of the same pack of 20 cards the following day.

Am I correct in saying that the odds of me picking the same card is a multiple of the single odds?

So 1/20 x 1/20 = 1/400

?

Because I've someone telling me the odds are still 1/20 that I'll pull the same card.

Teams, not trans! 😆

StatisticallyChallenged, that sounds the most miserable game of corners ever.

When I've played it, we move because there's music to dance to between each draw, nothing to do with probabilities!

mummmy2017

I'm not sure any betting shop offers bets on coin tosses, either.

But it is the best analogy I can think of for coin-tosses.

If you're in a hurdle race, with a course of 10 hurdles, with 1023 other people, then, everything else being equal, you are at 1/1024.

If after the nineth hurdle, there are only two people, you and one other, left, you won't be at 1/1024 any more, and no-one would give those odds as you ran for the tenth hurdle.

Did Op ever manage to successfully pull their first card?

The problem with probability is not the maths it is the English.

And Monty Hall, he is a cheat, he knows where the car is but has the slick chat of a second hand car dealer. This bit of information always makes students better able to understand the problem.

Because I like my door.
It's red , I like red.
When you know door 3 has better odds there is no guarantee it will win.
So I will stick with my door.
With no knowledge just facing two doors you have a 50/50 chance of a win.
Knowiñg the 33/67 thing.
Your only losing one chance to win.
Enough that I will chance it for once.
However if your on a 100 shows then that is 33 chance to loose. So you swap to his door.

#PotholeParadise
Yes as each person falls out of the race your odds of winning improve, till your odds are 1/2.
But unless you have a TARDIS how are you going back in time to place the bet?

Mummy, sorry to give a grim scenario, but if you needed a lift in a taxi and there was a 33.3% chance of having a crash in Taxi A and a 66.6% chance of having a crash in Taxi B, which one would you choose?

So mummy do you accept that by not swapping (on your one and only game), you are more likely to lose and the only reason you are sticking is because you like the colour red, more than you'd like to win a car?

No-one is going back in time. People watching at the bookies or betting online are making new bets, as the race progresses.

As each hurdle is faced the runners numbers dwindle.
The betting company use this info to calculate the odds.
So as less people are still jumping the odds on you winning increases, till there are only two of you left.
The 1024 odds were based on before the race , by refusing to accept they will decrease as you progress you are admitting to not understanding probability.

You take the safer car , but the doors hold no threat of death, so like many you can risk the lower odds for one show.
However for many shows you swap.

The 1024 odds were based on before the race , by refusing to accept they will decrease as you progress you are admitting to not understanding probability.

I think you stole my line here.

So, right, if you agree that the odds change as other possible outcomes are eliminated, can you see the comparison between the odds of tossing tails 10 times (TTTTTTTTTT= 1/1034) at the start,
and the odds of tossing Tails again, after you've got 9 Tails in a row?

Once you've got a tails nine times, it's like you're in that race, and with one hurdle to go. It's 50/50 whether you get ten in a row, after you've got nine tails.

But you need to get nine T in the first place it is a reverse if the race, each time you throw a T your odds of the next being a T double.

From someone else's link.
See two different questions.

Yes, it explains why you have been consistently wrong for pages now.

For the avoidance of doubt.

Everyone agrees with the answer to question 1 in the above graphic.

For pages, everyone except for you has agreed with the answer to question 2.

You, on the other hand, have been arguing that, having already got 6 heads in a row, the coin is more likely than not to land on tails on the 7th toss. According to you, the outcome of the previous tosses affect the next one.

Here's hoping the penny has finally dropped, regardless of what side it lands on...

Thank you for admitting I am right.
True the page does agree that if your after wins in a row your going to find it harder and harder to do .

any sequence of events gets harder to do the more you do it, because the probability multiplies by a number smaller than 1 each time. It's just as difficult to throw 10 heads in a row as it is to throw HHTHTTTHTH because the probability of you getting what you want on each throw multiplies by 0.5 each time, regardless of whether you now want to throw a heads or a tails.

Although you could use your earlier logic to contradict yourself. I either throw 10 heads in a row or I don't, so I have a 50/50 chance of throwing 10 heads in a row, not 1/1024

Late to this joyful party I know but would thinking about the coin toss like this help? If someone else tossed 9 heads in a row then put the coin down and you picked the coin up and tossed it. what are your odds of heads? Do you think the coin retains the memory of the previous persons actions?

True the page does agree that if your after wins in a row your going to find it harder and harder to do

It is hard to get wins in a row. Obviously.

However, we are not betting on that.

We are betting on a win. Or a loss.
We are not betting on wins in a row.
That's already happened.

Let's look at the what could happen in a week.

There could be 4 wins in a row.
WWWW - do you agree that is possible?

It has happened.

So the next day it could be win or lose.

So the 2 outcomes are:
WWWWW

Or

WWWWL

Using a simple tree diagram if you want, which of those 2 events are more likely to happen?

Given that we the unlikely event of 4 wins have already happened?

When you know door 3 has better odds there is no guarantee it will win

You are right that door 3 has better odds and there is no guarantee it will win. But if you understand probability as you claim to do, you will accept that if you changed doors you are twice as likely to win than if you stuck with your door.

Regardless of what happened the day before.
Regardless of how many wins there had been before.

You will ALWAYS have twice as much chance of winning if you swap.

You definitely do not have a 50 / 50 chance of winning, given there are 2 doors.

Because of prior knowledge.

Nobody has argued that it's not hard to throw 10 tails. But the trials are independent, and the coin has no memory, so the probability of you getting a tail on each consecutive throw does not vary in any way from 1/2. As you throw each tail the probability that you will achieve your 10 in a row increases, as you now only have to throw 8, 7, 6, 5... The probability of achieving 10 given you've already got 5 of them (for example) is exactly the same as the probability of just achieving 5. That is the point everyone has been trying to make...

The 1024 odds were based on before the race , by refusing to accept they will decrease as you progress you are admitting to not understanding probability

OMG - watch a horse race. Watch Betfair Exchange

Yes, the odds do change as the race progresses, because it's dependant on what happens. The horses skill becomes apparent and other events have influenced it.

But if there are 2 horses left, the odds on each one are still not evens.

One horse will still have more money on it than another horse.

Going back to the Monte Carlo issue.

If there were 25 blacks in a row and people were putting £100, 000 on red coming up and £1 on black coming up next, that means that people are overwhelmingly backing red to come up next. In a sense, they are making the odds on black coming up next 100,000 to 1.

Which does not make sense when there is a roulette wheel with 18 blacks and 18 red segments.

You take the safer car , but the doors hold no threat of death, so like many you can risk the lower odds for one show
However for many shows you swap

I don't know how to convince you anymore.

But yes - it's a good thing you don't gamble.

It's just as difficult to throw 10 heads in a row as it is to throw HHTHTTTHTH because the probability of you getting what you want on each throw multiplies by 0.5 each time, regardless of whether you now want to throw a heads or a tails.

And this is what @mummy2017 can't grasp. The odds of predicting 10 coin flips in advance are the same, regardless of 10 heads, 10 tails, or a mixture decided in advance.

On average, you will need 1024 flips to hit HHHHHHHHHH. But you will also need 1024 flips to hit TTHTHHTHHT.

The reason someone hasn't won the lotto 2 weeks running isn't because they are less likely to win in week 2 having won in week 1. They haven't won 2 weeks running in the same way that Mrs Jones from 40 Acacia Ave, Ipswich followed by Mr Peters from 2, High Chase, Truro, haven't won in that order. Because predicting who will win the lotto in successive weeks is nigh on impossible.

@mummy2017, please stop. At what point, with so many people with serious maths qualifications telling you that you're wrong, might you consider the possibility that you are, actually, wrong???

Because this is not maths.
This is an English problem.
Your refusing to understand that.
The show knows that on a ten week run the odds of 10 wins in a row is 1/1024.
For 10 wins to happen each show MUST be a win . Agreed?
So while each show has two doors with probability of 1/3 and 2/3.
The show is listed as a win or no win 1/2.
The coin toss....
I was also told in the race it was 1/2 at the last. Which I agreed with. The 1/1024 were for the start.

You don't necessarily have a 1/2 chance of winning at that point. If you and the other remaining runner are neck and neck and both equally good at running then you have a 1/2 chance. If the other person is an olympic runner then you still might only have a 1/10 chance of winning. They have the other 9/10.

Just because there are two possible outcomes does not mean they have an equal probability of occuring.