High School Coin Tossing: Binomial Distribution Explained

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SUMMARY

The discussion centers on the application of the binomial distribution to coin tossing, specifically when flipping a coin three times. The probability of obtaining k heads in n trials is defined by the formula: prob(k successes in n trials) = &binom{n}{k}p^k(1-p)^{n-k}, where p represents the probability of success on a single trial. For a fair coin, p is 1/2. This formula allows for the calculation of probabilities for various outcomes in binomial experiments.

PREREQUISITES
  • Understanding of binomial distribution
  • Familiarity with probability theory
  • Knowledge of combinatorial mathematics
  • Basic statistics concepts
NEXT STEPS
  • Study the derivation of the binomial distribution formula
  • Learn about the properties of binomial coefficients
  • Explore applications of binomial distribution in real-world scenarios
  • Investigate the differences between binomial and other probability distributions
USEFUL FOR

Students and professionals in statistics, data science, and mathematics who seek to understand probability distributions and their applications in experiments involving binary outcomes.

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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