Probability problem for statisticians/mathematicians

[expat]

Isn't this more akin to a poisson distribution where the expected number of failures is 2?

So the probability of k failures is power(2, k) * power(e, -2) / k! ??

I think so. Poisson is where independent events come along independently, right? (It's been a while).

Anyway, the point is that with the goats and doors (or whatever variant of the TV show), the events are not independent: there is a known fixed number of goats, so if one is behind door 10 then it isn't behind doors 1-9. Knowing what is behind door 10 therefore does tell you something about what's behind the other doors.

With independent events, knowing how one trial comes out tells you nothing about other trials.

(Of course if your first 9 vehicles all exploded on take-off, you would begin to formulate a hypothesis about the likely outcome of launch 10; but that's inference, not probability).

[BrilloPad]

I think so. Poisson is where independent events come along independently, right? (It's been a while).

Anyway, the point is that with the goats and doors (or whatever variant of the TV show), the events are not independent: there is a known fixed number of goats, so if one is behind door 10 then it isn't behind doors 1-9. Knowing what is behind door 10 therefore does tell you something about what's behind the other doors.

With independent events, knowing how one trial comes out tells you nothing about other trials.

(Of course if your first 9 vehicles all exploded on take-off, you would begin to formulate a hypothesis about the likely outcome of launch 10; but that's inference, not probability).

Off Topic but something I have always thought about - the swap on "deal or no deal". Would you swap? I think it makes no difference - but I would not swap anyway. Just in case I gave away the wrong box.

[Bagpuss]

If there is a say 1 in 10 chance of something failing that doesn't equate to 100% chance of failure after 9 successful attempts. Similarly you could throw a coin 2 times which lands on heads it doesn't make tails more likely the next throw. All the lies damn lies and statistics, is a belief based on misunderstanding/misinterpretation/manipulation, that doesn't come into probability theory, it's usually the mistake the media make with basic statistics.

[Diver]

If there is a say 1 in 10 chance of something failing that doesn't equate to 100% chance of failure after 9 successful attempts. Similarly you could throw a coin 2 times which lands on heads it doesn't make tails more likely the next throw.

and there is always a possibility that the coin may never come down again

[Bagpuss]

and there is always a possibility that the coin may never come down again

But that is not an event outcome. If you want the probability of something happening to a coin then thats different

Re Deal or no Deal, the ultimate example of idiocy over calculated odds. It's a stupid game of effectively coin tossing, but at each deal you can calculate odds of potential winnings> offer, when those fall to <0.5 it's a good time to deal.

[Diver]

But that is not an event outcome. If you want the probability of something happening to a coin then thats different

Re Deal or no Deal, the ultimate example of idiocy over calculated odds. It's a stupid game of effectively coin tossing, but at each deal you can calculate odds of potential winnings> offer, when those fall to <0.5 it's a good time to deal.

Las Vegas here I come

[Bagpuss]

Las Vegas here I come

IIRC Blackjack has the best odds of winning apparently.
I like a little flutter myself, at the start of the football season you often get stupid odds on singles games e.g. a couple of years ago Middlesborough were 10-1 to beat Arsenal away. Those odds didn't seem representative of the chance in a 3 outcome game. Anyway Boro won and so did I.

The bookies know what they are doing though, once the season gets into full swing those type of 'promotional' odds vanish.

[Diver]

IIRC Blackjack has the best odds of winning apparently.
I like a little flutter myself, at the start of the football season you often get stupid odds on singles games e.g. a couple of years ago Middlesborough were 10-1 to beat Arsenal away. Those odds didn't seem representative of the chance in a 3 outcome game. Anyway Boro won and so did I.

The bookies know what they are doing though, once the season gets in to full swing those type of odds vanish.

Along with the punters money

[Bagpuss]

Along with the punters money

These days you can beat the bookie. With free bets their is a method where you can't lose (profits not high though). These days you can be the bookie and lay bets. Occasionally with transatlantic betting e.g. Hatton V Mayweather you can get odds on and odds against on the same fight which means you can't lose.

[Diver]

A man wanted to get into his work building, but he had forgotten his code. However, he did remember five clues. These are what those clues
were:

1. The fifth number plus the third number equals fourteen.
2. The fourth number is one more than the second number.
3. The first number is one less than twice the second number.
4. The second number plus the third number equals ten.
5. The sum of all five numbers is 30.

What were the five numbers and in what order?