Heads or tails? (Question from Feynman lectures)

In summary: Feynman later attended these lectures, and then added some material to these chapters, and then these two lectures were added to FLP Vol. III (Chapter 14, I think) with notes added by Feynman.
  • #1
#neutrino
51
2
I have been going through feynmans lectures on probability and have a few questions that i can't answer ; in the part regarding fluctuations he introduces us to tree diagrams(pascals triangle ) and gives an example regarding the toss of a coin
If we consider the no. Of tosses as n and no. Of heads as k then it can be given as
( n) n!
( k ) = ----
k!(n-k)!
I know that n! Represents n factorial and the fact that probability is generally
Given by
Probability = highest estimate of an event
----------------------------
Total no. Of events
However what i don't get is why do we multiply k! By (n-k)! Souldnt it be n! In the denominator and k! In the numerator ?
I know it has something to do with the triangle however unable to figure it out
 
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  • #2
#neutrino said:
I have been going through feynmans lectures on probability and have a few questions that i can't answer ; in the part regarding fluctuations he introduces us to tree diagrams(pascals triangle ) and gives an example regarding the toss of a coin
If we consider the no. Of tosses as n and no. Of heads as k then it can be given as
( n) n!
( k ) = ----
k!(n-k)!
I know that n! Represents n factorial and the fact that probability is generally
Given by
Probability = highest estimate of an event
----------------------------
Total no. Of events
However what i don't get is why do we multiply k! By (n-k)! Souldnt it be n! In the denominator and k! In the numerator ?
I know it has something to do with the triangle however unable to figure it out
The equation is (n)= n!
(k) -----
k!(
 
  • #3
The equation is (n)= n!
-----
k!(n-k)!
 
  • #4
You're actually asking, I think, about how many ways you can get ##k## heads from ##n## coin tosses. And why the answer is ##\frac{n!}{(n-k)! k!}##

You could start by taking ##n = 5##, say, and counting all the ways you can get ##k = 0, 1, 2, 3, 4## and ##5##.

Then see whether that fits the formula, and why.
 
  • #5
BTW (just in case anyone is interested), this was not Feynman's lecture, but Matt Sands' lecture. Feynman had to go out of town on some business for a week, so Matt Sands gave the lectures that became FLP Vol. I Chapters 5 and 6.
 
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What is the probability of getting heads or tails when flipping a coin?

The probability of getting heads or tails when flipping a coin is 50%, assuming the coin is fair and there are no external factors that could influence the outcome. This is because there are only two possible outcomes and they are equally likely to occur.

Why is it called "heads or tails"?

The terms "heads" and "tails" refer to the two sides of a coin. In the past, coins were often stamped with the head of a ruler or deity on one side and the tails or emblem of the issuing authority on the other side.

What is the significance of "heads or tails" in probability theory?

"Heads or tails" is a common example used in probability theory to illustrate the concept of a random event with two equally likely outcomes. It is also used as a simple example to demonstrate the principles of probability and statistical analysis.

How many times should I flip a coin to get an equal number of heads and tails?

There is no specific number of times you should flip a coin to get an equal number of heads and tails. Each flip is an independent event and the outcome is not affected by previous flips. However, the more times you flip the coin, the closer the ratio of heads to tails is likely to approach 1:1.

Are there any strategies or tricks to increase the chances of getting heads or tails?

No, there are no strategies or tricks that can increase the chances of getting heads or tails. Each flip of a fair coin will always have a 50% chance of landing on either heads or tails, regardless of any previous outcomes.

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