Coin Tossing: Binomial Distribution Explained

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Discussion Overview

The discussion revolves around the concept of binomial distribution in the context of tossing a coin multiple times. Participants explore the probability of obtaining a certain number of heads in a specified number of trials, addressing both theoretical and practical aspects of the distribution.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants express confusion about why tossing a coin three times is associated with binomial distribution.
  • Questions are raised regarding the probability of flipping k heads in n trials.
  • One participant suggests that the probability of getting heads in a single flip is 1/2, while others discuss the implications of this probability in the context of binomial distribution.
  • Another participant provides the formula for binomial probability, stating that it is given by ##\binom{n}{k}p^k(1-p)^{n-k}##, where ##p## is the probability of success on one trial.
  • There is repetition of the binomial probability formula, emphasizing its relevance to the discussion.
  • Participants acknowledge the formula's application specifically for fair coins, where ##p=1/2##.

Areas of Agreement / Disagreement

Participants generally agree on the formula for binomial distribution and its application to coin tossing, but there is some confusion regarding the initial understanding of the concept and its implications.

Contextual Notes

Some assumptions about the fairness of the coin and the definition of success in trials are present but not fully explored, leading to potential gaps in understanding.

Who May Find This Useful

This discussion may be useful for individuals seeking clarification on binomial distribution, particularly in relation to probability theory and its application to simple experiments like coin tossing.

CaptainX
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Why tossing a coin three times is said to have binomial distribution? I'm little bit confused.
 
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What is the probability to flip k heads in n trials?
 
CaptainX said:
Why tossing a coin three times is said to have binomial distribution? I'm little bit confused.
What is confusing?
 
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fresh_42 said:
What is the probability to flip k heads in n trials?
I think it's 1/2
 
CaptainX said:
I think it's 1/2
It doesn't matter if it's a fair coin or not. Say one coin flip has probability ##p## for heads. Now what is the probability of ##k## heads in ##n## flips? How any possibilities are there for ##k## out of ##n## and what is the combined probability?
 
Binomial: prob (k successes in n trials) ##=\binom{n}{k}p^k(1-p)^{n-k}## where ##p## is the probability of success on one trial. For fair coins ##p=1/2##.
 
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mathman said:
Binomial: prob (k successes in n trials) ##=\binom{n}{k}p^k(1-p)^{n-k}## where ##p## is the probability of success on one trial. For fair coins ##p=1/2##.
... which is the answer to the question.
 
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mathman said:
Binomial: prob (k successes in n trials) ##=\binom{n}{k}p^k(1-p)^{n-k}## where ##p## is the probability of success on one trial. For fair coins ##p=1/2##.
Thank you very much!
 

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