Binomial Probability (1 Viewer)

[Rainbowtopp]

Any and all help appreciated!

'What is the most likely number of head's when a coin is tossed (i) 50, (ii) 100 times?'

Apart from calculating the probability for every possible result eg. 1 head, 2 heads, 3 heads etc, is there any simpler method?

Thanks!

 

[Carrotsticks]

Have you done the topic 'Greatest Coefficient' yet?

Oh and to answer your question, the most likely number of times to get heads is the 'floor function' of



Where A = number of times you toss the coin.

What I mean by 'floor function' of a number is the nearest integer rounded down.

So for example, the floor of 2.3 is just 2.

 

[braintic]

Have you done the topic 'Greatest Coefficient' yet?

Oh and to answer your question, the most likely number of times to get heads is the 'floor function' of



Where A = number of times you toss the coin.

What I mean by 'floor function' of a number is the nearest integer rounded down.

So for example, the floor of 2.3 is just 2.

But for 50 tosses that would give 25 heads. Why is 25 more likely than 26?

 

[Carrotsticks]

Because the probabilities are spread across a binomial distribution curve that is perfectly symmetrical at x=25. We have symmetry because the object we are using has 0.5 probability for either outcome.

But say we used a die, the peak would be towards the left more.

So the general formula is floor of (a+1)/b, where b is the number of possible outcomes. For example, if the object were a die, then b=6.

If (a+1)/b is an integer (or in other words if a+1 is divisible by 6), then you'll have that value as well as the next consecutive integer being the most likely result.

Since 51 isn't divisible by 6, our 'curve' (apostrophe because we don't actually have a curve, just points that we plot since we are using discrete values), does not have a plateau, but an actual peak, which occurs precisely at 25.

 

[braintic]

Because the probabilities are spread across a binomial distribution curve that is perfectly symmetrical at x=25. We have symmetry because the object we are using has 0.5 probability for either outcome.

But say we used a die, the peak would be towards the left more.

So the general formula is floor of (a+1)/b, where b is the number of possible outcomes. For example, if the object were a die, then b=6.

If (a+1)/b is an integer (or in other words if a+1 is divisible by 6), then you'll have that value as well as the next consecutive integer being the most likely result.

Since 51 isn't divisible by 6, our 'curve' (apostrophe because we don't actually have a curve, just points that we plot since we are using discrete values), does not have a plateau, but an actual peak, which occurs precisely at 25.

Don't worry, I was being an idiotic, forgetting to include n=0 when considering symmetry.

 

[anomalousdecay]

Don't worry, I was being an idiotic, forgetting to include n=0 when considering symmetry.

You weren't being an idiot. You were just showing us the reason behind it

Smart idea.

 

[braintic]

You weren't being an idiot. You were just showing us the reason behind it

Smart idea.

It looks like there was method in my madness after all!

 

[Rainbowtopp]

Thank you all so much!