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Original poster

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

999 replies

Fainne · 24/01/2020 00:23

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.

OP posts:
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8
mummmy2017 · 26/01/2020 00:01

But you didn't win 25 times.
You only played once .
This has only happened once ever.
And someone would have bet on the 26th ball winning them some money and collected.

chomalungma · 26/01/2020 00:03

How do I start a casino?

Looks like a good way to make money off people who don't understand maths,

I could just start with a roulette table.

StatisticallyChallenged · 26/01/2020 00:05

You could do well starting one with 3 doors....

mummmy2017 · 26/01/2020 00:06

Yes, I did read that.
Chance, because the swap give you a better one, but what if I got the right door too start with.
I will leave the show with or without a car. 1/2 odds. It is just the probability on the swap is better but not guaranteed.

iseetodaywithanewsprintfray · 26/01/2020 00:06

"But you didn't win 25 times.
You only played once ."

But if you had won 25 times you think the odds would be different?

chomalungma · 26/01/2020 00:07

But you didn't win 25 times

The point is that people weren't gambling on a run of 26 black balls.

But they saw that it had come up black lots and so they started putting more money on red because 'it must come up'.

If £100,000 was put on red and £10,000 was put on black, then the casino is going to clear up as that is a 10 / 1 difference on 1 / 2 odds.

Yes, eventually someone got lucky. But the odds of it being black or red each time never changed.

iseetodaywithanewsprintfray · 26/01/2020 00:08

"I will leave the show with or without a car. 1/2 odds. It is just the probability on the swap is better but not guaranteed."

To be clear, 1/2 odds actually means a 66% probability, it does not mean a 50/50 chance.

And no, it is not guaranteed. It is more likely that you would leave with the car if you swapped though, so why wouldn't you do that? Just because there are two choices does not make it a 50/50 chance.

mummmy2017 · 26/01/2020 00:09

I don't gamble because I do understand probability.
No way would I ever bet to win ten games of chance in a row.
Unless your offering 1/1 odds.

DustyDood · 26/01/2020 00:10

@mummmy2017

As you say, "the probability on the swap is better but not guaranteed" that's right, so why wouldn't you swap? Why wouldn't you go with the better probability?

chomalungma · 26/01/2020 00:11

Chance, because the swap give you a better one, but what if I got the right door too start with

I will leave the show with or without a car. 1/2 odds. It is just the probability on the swap is better but not guaranteed.

It is not 1 in 2 of you winning.

There is a 1 in 3 chance of you winning first time if you don't change.
Reasonable odds

There is a 2 in 3 chance of you losing if you don't change.

So if you win first time, then take the car.

mummmy2017 · 26/01/2020 00:11

Your either going to win or loose.
How is that not 1/2.

iseetodaywithanewsprintfray · 26/01/2020 00:11

"I don't gamble because I do understand probability."

I hate to break this to you, but...

iseetodaywithanewsprintfray · 26/01/2020 00:12

"Your either going to win or loose.
How is that not 1/2."

Because... because of probability.

chomalungma · 26/01/2020 00:12

No way would I ever bet to win ten games of chance in a row.

But that's not the question.

If you had won 9 games in a row, would you bet £10 on winning the next one? If you won, I would give you £1. If you lost, you would give me £10.

I don't gamble because I do understand probability

You don't.

iseetodaywithanewsprintfray · 26/01/2020 00:14

"Your either going to win or loose.
How is that not 1/2."

Tomorrow morning I will be dead or alive. Do you give me a 50/50 shot of making it through the night?

chomalungma · 26/01/2020 00:14

Your either going to win or loose

I buy a lottery ticket.
I could win or lose
Do I have a 1 in 2 chance of winning?

(I used to be a primary teacher. I saw something like this on a Year 5 answer. What are the chances of getting a 6? They said 50%. Because you either got a 6 or you didn't)

mummmy2017 · 26/01/2020 00:15

Your talking short odds.
I am talking long odds.
Not the same thing.
Also there are two doors.
One may have better odds to win.
But you still only have a winning door and a loosing door. The third door is no longer there for you to choose.

chomalungma · 26/01/2020 00:18

But you still only have a winning door and a loosing door. The third door is no longer there for you to choose

Haven't we already been over this?

Ok.

In the rugby, there are 6 teams.
I can tell you that Italy have never won the 6 Nations.

I will give you odds of 100 / 1 on Italy winning the 6 Nations.
That's reasonable, given there are 6 teams so there is a 1 i 6 chance of them winning.

Isn't it?

lotsofoysters · 26/01/2020 00:18

Your talking short odds.
I am talking long odds.

You're talking something...

iseetodaywithanewsprintfray · 26/01/2020 00:20

Whether we talk long odds or short odds, 1/2 or 2/1 is not the same as 50/50.
If one door has better odds to win, it's not a 50/50 shot, is it?

chomalungma · 26/01/2020 00:20

One may have better odds to win

Yes, One does have better odds to win.
And you are aware of that when you get to choose.

Which has been mentioned on this thread a few times.

mummmy2017 · 26/01/2020 00:26

But your taking Italy's past performance into account on the 1/100.
If all the teams were equal then the 1/6 is fine.
Just like I was saying on the coin toss. The past does influence the odds .
The doors comes down to in the end there is more chance that door 3 has the car but it is not a 100% chance . This could be the day the 33% wins .

DustyDood · 26/01/2020 00:27
  1. If you chose the car door you lose by swapping.
  2. If you chose a goat door, you win by swapping.

Chance that scenario 1 happened: 1/3
Chance that scenario 2 happened: 2/3

Therefore swapping always gives you a better chance of winning.

iseetodaywithanewsprintfray · 26/01/2020 00:28

"Just like I was saying on the coin toss. The past does influence the odds ."

Only if the events are not independent. Coin tosses and door picks are independent.

lotsofoysters · 26/01/2020 00:29

One may have better odds to win.
But you still only have a winning door and a loosing door.

But knowing the odds, why wouldn't you pick the door with the higher outcome of winning?

If you played 90 games and never switched doors, you'd win the car 30 times on average.
If you switched every time, you'd win the car 60 times on average.
If you let a computer randomly pick a door for you each time, you'd win 45 times on average.