Do The Math!

[woof!]

Artie may try to pull fast ones on us on this forum, but I'd trust him to make honest change as a cashier. Hung on the other hand has forfeited all right to be accorded that confidence.

As has Chuckie.

The Liar's Club back in 2002, I gotta give 'em credit, they weren't in Hung & Chuckie's league. And that's not even an insult, I'm complementing Hung & Chuckie on the talent they're manifestly proudest of.

--Toto

 

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[hung]

Now, I wonder why in the world you put 1/2 for that 4th event in the series, unless you completely agree with Rudy?

Once again and sincerelly hoping that you finally understand.

The chances for flipping a coin and heads appear is 1/2 (50%). There are only two possible results: heads or tails.
As isolated and independent variable event, the act of flipping a coin means 50% probability for either result.
But Dr. Rudy stated this:
'If you flipped the coin three times and got heads, what are the chances that if you flipped it again a head would appear?Well it's 50%.'

Notice that this is different. He is clearly stating that the coin was previously flipped 3 times and heads appeared. Then he asks what the chances are that heads come out again in the fourth flip.
These are no longer independent and isolated variable events. He linked the previous 3 flip results to a fourth event. And no way the fourth flip will be 50% as you can see that each time you flip a coin for an exact desired result, chances diminish.
So:
1/2*1/2*1/2*= 1/8 = 12.5%. This is the probability that heads would come out in all 3 flips which is already achieved in his example, and in order to achieve the result for heads again in a fourth flip, you need to multiply the result again for 1/2 or 50%. The correct result is 6.25% chances that heads will come out again in a fourth flip.

If he had another thing in mind and misexpressed himself or not I don't know. What I do know is that his example is wrong and I demonstrated this to him. And in order to know how he was thinking in the process I posted that second problem for him to solve, but he declined. So in my opinion, his binomial distribution view is inacurate. In probability, one has to fully interpret the problem and not just rely on formulas. In fact you can solve those kind of problems with no formulas at all. Just logical thinking.

I hope this explanation finally suffices and now I think it becomes simple to solve the second problem I posted.

Flip a coin until you obtain heads in the second time. What is the probability that the coin is flipped 4 times?

There is only one answer possible and I assure you it's not 50%.
If you understood well what I explained above, it's easy to solve this simple quiz. Just interpret it.
Will you try it or will you back out as all the others?

 

[Rudy(CA)]

Now, I wonder why in the world you put 1/2 for that 4th event in the series, unless you completely agree with Rudy?

Once again and sincerelly hoping that you finally understand.

The chances for flipping a coin and heads appear is 1/2 (50%). There are only two possible results: heads or tails.
As isolated and independent variable event, the act of flipping a coin means 50% probability for either result.
But Dr. Rudy stated this:
'If you flipped the coin three times and got heads, what are the chances that if you flipped it again a head would appear?Well it's 50%.'

Notice that this is different. He is clearly stating that the coin was previously flipped 3 times and heads appeared. Then he asks what the chances are that heads come out again in the fourth flip.
These are no longer independent and isolated variable events. He linked the previous 3 flip results to a fourth event. And no way the fourth flip will be 50% as you can see that each time you flip a coin for an exact desired result, chances diminish.
So:
1/2*1/2*1/2*= 1/8 = 12.5%. This is the probability that heads would come out in all 3 flips which is already achieved in his example, and in order to achieve the result for heads again in a fourth flip, you need to multiply the result again for 1/2 or 50%. The correct result is 6.25% chances that heads will come out again in a fourth flip.

I'll repeat myself again, verbatim.

If you flipped the coin three times and got heads, what are the chances that if you flipped it again a head would appear? Well, it is 50%.
The coin holds no prior history of the previous tosses and each toss has a 50 50 chance of coming up heads.

Note I said: "What are the chances that if you flipped it again a head would appear? Well, it is 50%." Which is exactly correct. Each flip is independent and the fact that the previous flips had produced heads does not change the outcome probability of the current flip. Note that the question specifically asked about the odd of the current flip.

Later on in my post I said

Note from the above sequence of 4 tests, the average probability of getting four successes is 1/16 or 6.25%.

 

[Carl-NC]

The chances for flipping a coin and heads appear is 1/2 (50%). There are only two possible results: heads or tails.

That's what Rudy said!

As isolated and independent variable event, the act of flipping a coin means 50% probability for either result.

That's what Rudy said!

But Dr. Rudy stated this:
'If you flipped the coin three times and got heads, what are the chances that if you flipped it again a head would appear?Well it's 50%.'

Yes, and you just agreed. Twice even.

Notice that this is different. He is clearly stating that the coin was previously flipped 3 times and heads appeared. Then he asks what the chances are that heads come out again in the fourth flip.
These are no longer independent and isolated variable events. He linked the previous 3 flip results to a fourth event. And no way the fourth flip will be 50% as you can see that each time you flip a coin for an exact desired result, chances diminish.

This is where your HungLogic is kicking in. A coin has no idea what has happened in the past. The odds of a particular flip landing H or T is independent on what happened the last time it landed. This is Stats 101.

P(H) = 50% no matter what happened before. For a series, it is true that P(H,H,H,H) = 6.25%, the same as P(L,L,L,H). I can rewrite this as P(H,H,H)*P(H); P(H,H,H) is 12.5%, but the fourth flip still has P(H) = 50%. That's clearly what Rudy said. And you agreed, until you got totally confused between P(event) and P(series). Rudy did not ask how the fourth flip affected P(series), only the P(event) of the fourth flip itself. And it wasn't even a trick question!

 

[EE THr]

Speaking of predictability, See #33, in Predictable Pattern of Con Artists.

Prediction made.

Prediction proven.




Thanks, hung-up!

 

[hung]

A coin has no idea what has happened in the past.

Did I state it does?

The odds of a particular flip landing H or T is independent on what happened the last time it landed. This is Stats 101.

That's what hung said!

BUT, Mr.Doc said that the SAME coin had HEADS in the three previous flips and ask the chances for a fourth HEAD in a fourth flip.
Do you really think it's 50%??
If you do, you do not know anything about Probabilities. In fact if any of you did, my question had already been answered since the first minute it was posted.
Now, to end this soap opera for good, PLEASE solve the quizz, IF YOU REALLY KNOW about the simple binomial distribution you, Dr. Rudy, or anybody who knows about it, will solve it in 35 seconds. NO KIDDING.
Heck, I did not post any more complex distribution such as T-student, Poisson, Paschal, Hypergeometric, etc. It's a simple DUMB question.
DO IT and if you do it RIGHT, you will know which one of us is right.

DO THE MATH!

Flip a coin until you obtain heads in the second time. What is the probability that the coin is flipped 4 times?

 

[Carl-NC]

A coin has no idea what has happened in the past.

Did I state it does?

Yes, you did:

But, when you flip the same coin with prior results on record and clearly stated it was 'heads' in all 3 flips and you want the chances that heads show up again in a fourth try, no way it will be 50%. Each time a flip is made the chances DIMINISH.

BUT, Mr.Doc said that the SAME coin had HEADS in the three previous flips and ask the chances for a fourth HEAD in a fourth flip.
Do you really think it's 50%??

I don't have to think it is, I know it is. The overall probability of a "streak" diminishes with each flip, but the probability of each flip is still 50%. That's all Rudy claimed. Nothing more.

Flip a coin until you obtain heads in the second time. What is the probability that the coin is flipped 4 times?

Already answered that one. P(T,T,T,H) = 6.25%. But so is P(T,T,T,T)... why do you think that is?

There is a pretty good reason why everyone disagrees with you on this, including those who remain suspiciously quiet on the matter. Had you ever actually taken a course in statistics, you would understand what's going on, or you would have flunked.

 

[woof!]

the "we couldn't have made this up" dept.

Flashbulb, the average 8-year-old kid can get the answer right. 50%.

It would not have occurred to us to claim that you were so confused by reality to have predicted that a simple problem like this would totally confound you, and yet here you are leaving absolutely no doubt in the matter even though you have repeatedly stated the premise of the problem correctly. If you think it's gonna take a mere 35 seconds worth of calculating the binomial distribution to figure it out, then you're 'way too slow: the answer is 50% and it doesn't take any math to arrive at that answer.

Have you noticed that your usual fan club has deserted you on this one? It's because even they know it's 50%!

Perhaps you'd like to do the math for Chuckie's next patent.

--Toto

 

[hung]

Flip a coin until you obtain heads in the second time. What is the probability that the coin is flipped 4 times?

Already answered that one. P(T,T,T,H) = 6.25%. But so is P(T,T,T,T)... why do you think that is?

Are you saying that the answer to my question is 6.25%? Is that it?

Had you ever actually taken a course in statistics, you would understand what's going on, or you would have flunked.

In my Country everyone who is in a selective process for a job in the government is required to take tests in 20 superior subjects. Statistics being one of them. Actually Advanced Statistics.
Incidentally, the question I posted above was included in one of the previous examinations. A very easy one actually.

 

[Rudy(CA)]

In my Country everyone who is in a selective process for a job in the government is required to take tests in 20 superior subjects. Statistics being one of them. Actually Advanced Statistics.

Sorry to hear you didn't get the government job.

 

[EE THr]

Flip a coin until you obtain heads in the second time. What is the probability that the coin is flipped 4 times?

Already answered that one. P(T,T,T,H) = 6.25%. But so is P(T,T,T,T)... why do you think that is?

Are you saying that the answer to my question is 6.25%? Is that it?

Are you asking if he is saying that?

Am I asking you if you are asking if he's saying that?

Is there no end to your nonsense?

 

[Real de Tayopa Tropical Tramp]

Evening, I must agree with my friend CARL: he posted --> I don't have to think it is, I know it is. The overall probability of a "streak" diminishes with each flip, but the probability of each flip is still 50%.
************
We are speaking of two different goals or sequences.


Don Jose de La Mancha

 

[hung]

What's the matter Carl, you need more time to consult a Statistics teacher?
Is 6.25% your answer to my question or not?

Is it or not??

 

[Rudy(CA)]

I guess it's the nature of some people to just be argumentative.

 

[hung]

I guess it's the nature of some people to just be argumentative.

Dr. Rudy, since my last probability question might be too hard for you to solve, here's a simpler one.

'Four distinct coins are flipped. What's the probability of appearing 2 heads and 2 tails?'

C'mon. It takes only 15 seconds to do it. If you know probability distribution this is the time required for you to solve it.
Otherwise, you will leave this one blank too.
So...
What's gonna be?

 

[EE THr]

hung-up;

It takes only 15 seconds to do it....this is the time required for you to solve it.

An eight year old can solve that as he reads it.

I think you are operating on a different clock speed than everyone else.

But you are great entertainment. Are you the battery bunny's cousin? Let's see how long you can just keep going, and going, and going....

 

[Real de Tayopa Tropical Tramp]

Hi EE, remember your recent post on insults my friend ?? tsk tsk

Don Jose de La Mancha

 

[aarthrj3811]

You are correct Real Deal…We are speaking of two different goals or sequences…How come the first 3 flips were all heads ?

 

[Real de Tayopa Tropical Tramp]

hi AA, you posted --> How come the first 3 flips were all heads
**************
Cuz swr cheated a bit snicker. He knows how to toss em.

Don Jose de la Mancha

 

[Rudy(CA)]

I guess it's the nature of some people to just be argumentative.

Dr. Rudy, since my last probability question might be too hard for you to solve, here's a simpler one.

'Four distinct coins are flipped. What's the probability of appearing 2 heads and 2 tails?'

C'mon. It takes only 15 seconds to do it. If you know probability distribution this is the time required for you to solve it.
Otherwise, you will leave this one blank too.
So...
What's gonna be?

You still haven't admitted you were wrong on the other one. Why should I waste my time ?