Math question- help me calculate odds

AustinCBrown · Mar 9, 2008

Greetings all you math whizzes,

Can someone tell me what the odds of flipping tails on a coin 4.3 billion times in a row would be? I know you take 1/2 X 1/2 4.3 billion times to determine the answer, but I don't know how to, well, do it that many times on a calculator.

It's ten to the what power?

Many thanks for helping me. I need the answer for something I'm writing (fictional).

Austin

BarbaraKE · Mar 9, 2008

It would be .5 to the 4.3 billionth power.

Or (1 over (2 to the 4.3 billionth power) )

In other words, it's a very tiny number.

Julie Worth · Mar 9, 2008

Zero. The odds of getting tails just a hundred times is 7.89 x10^-31.

jclarkdawe · Mar 9, 2008

You wouldn't do this on a calculator. At one second per calculation, no breaks, you're looking at something like 135 years. If you live to 70, you've only got a little over 90,000,000 seconds to work with (think about all that time I've wasted answering this).

The answer would be so close to zero as to be meaningless.

Best of luck,

Jim Clark-Dawe

benbradley · Mar 9, 2008

BarbaraKE said:
It would be .5 to the 4.3 billionth power.

Or (1 over (2 to the 4.3 billionth power) )

In other words, it's a very tiny number.

You can convert 2 to the power of x into 10 to the power of something by multiplying x by the log of 2 base 10, or (the actual value to five significant figure) .30103 (check this out with smaller numbers: 2^10 = 1024, so the power of 10 should be 10 * 0.3 = 3. and indeed 10^3 = 1000, close enough), so it would be 1 over 10 to the 1.294 billion, or 1 / (10 ^ 1,294,000,000)

Indeed for virtually any practical purpose this number and calculation is meaningless, but for fiction it could certainly apply, and mathematically it is definitely not zero.

AustinCBrown · Mar 9, 2008

Need a little more help

Thanks all, but I need some clarification.

Imagine that I want to express the chances of flipping a coin that many times in row in terms like of being struck by lightning. For example, people say that you have, say, a 1 in 483,000 chance of being struck by lightning during your lifetime. Or, the chances of achieving a royal flush, for another example, is only 1 in 2,598,960 possible hands.

How can the coin flip thing be expressed in those terms... because I understand that

And could you round it up to a nice 10 to the X power? (10 to the 121 or 133 or ????).

Thanks,
Austin

IceCreamEmpress · Mar 9, 2008

How can the coin flip thing be expressed in those terms...

You have a one-in-10^1.294 billion chance. In other words, you have a one in 10-followed-by-1.294 billion zeros chance. There is no other name for this number. It is millions of times greater than the numbers of elementary particles in the observed universe.

Julie Worth · Mar 9, 2008

AustinCBrown said:
And could you round it up to a nice 10 to the X power? (10 to the 121 or 133 or ????).

1 in 10^1.3 billion, which is as close to zero as you could hope for.

It can be expressed as one chance in 10, followed by more than a billion zeros. The latter number is enormously bigger number than the number of particles in the universe, which is approximately 10 followed by 80 or so zeros.

Crimey! Ice Cream and I said exactly the same thing!

AustinCBrown · Mar 9, 2008

Thanks

Thanks all. That's exactly what I was looking for, even if it is a rediculously improbable number. Hopefully I'll finish the book I'm working on- which rests fundamentally upon that improbability- and hopefully it will be published, which, of course, is about as likely as 1 in 10^100 power

Austin

HeronW · Mar 11, 2008

In any coin flip it's not the number of times that gets heads or tails--it's every individual toss. Each toss has a 50/50 chance, period. The tosses are NOT cumulative which is what trips up gamblers every time thinking: I hit heads 50x the next has got to be a tail. WRONG! Physics and statistics aren't meshing. Depending on the surface, the coin could land edge up but the surface area of the edge vs the surface area of both sides, plus the stability of an edge landing etc, is quite lean, though it does happen--blowing the heads/tails question out of the water.

LIVIN · Mar 11, 2008

AustinCBrown said:
For example, people say that you have, say, a 1 in 483,000 chance of being struck by lightning during your lifetime.

Well, if this is correct, it's about an equal chance as being struck by lightning 8,902 times.

Julie Worth · Mar 11, 2008

LIVIN said:
Well, if this is correct, it's about an equal chance as being struck by lightning 8,902 times.

And lived!

hammerklavier · Mar 11, 2008

Julie Worth said:
And lived!

I think if you factor in the "and lived" into the probability the number of consecutive lightning strikes would come down considerably.

Math question- help me calculate odds

AustinCBrown

BarbaraKE

Julie Worth

What? I have a title?

jclarkdawe

Feeling lucky, Query?

benbradley

It's a doggy dog world

AustinCBrown

IceCreamEmpress

Hapless Virago

Julie Worth

What? I have a title?

AustinCBrown

HeronW

Down Under Fan

LIVIN

Julie Worth

What? I have a title?

hammerklavier

It was a dark and stormy night