Calculating the Probability of Getting k Heads from Flipping a Fair Coin n Times

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SUMMARY

The probability of getting k heads when flipping a fair coin n times is calculated using the formula (nCk) / (2^n). Here, nCk represents the number of combinations of n flips taken k at a time, and 2^n denotes the total number of possible outcomes from n flips. This approach is mathematically sound and aligns with the principles of combinatorial probability.

PREREQUISITES
  • Understanding of combinatorial mathematics, specifically combinations (nCk).
  • Basic knowledge of probability theory.
  • Familiarity with the concept of independent events in probability.
  • Ability to perform calculations involving powers of two.
NEXT STEPS
  • Study the concept of combinations in depth, focusing on the formula for nCk.
  • Learn about the binomial probability formula and its applications.
  • Explore the concept of independent events and their significance in probability calculations.
  • Practice calculating probabilities for various scenarios involving coin flips and other independent events.
USEFUL FOR

Students studying probability and statistics, educators teaching combinatorial mathematics, and anyone interested in understanding the fundamentals of probability calculations.

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Homework Statement

If I flip a fair coin n times, that is the probability that I get k heads?

Homework Equations

nCk: the combination in which order doesn't matter s.t one picks k from n.

The Attempt at a Solution

there are 2*2*2*2*2...*2=2^n total outcomes. but the event specifies k ways of picking heads out of n flips. So, (nCk)/(2^(n)). Is this correct? Intuitively, I think its sound.
 
Physics news on Phys.org
Yes, it's quite sound.
 

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