Is Flipping Coins Sequentially Different from Simultaneously for Probability?

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SUMMARY

The discussion centers on the probability of obtaining heads from flipping coins, specifically comparing sequential flips to simultaneous flips. Both scenarios involve flipping four coins, with the probability of landing heads twice calculated as 6/16. The key takeaway is that the independence of coin flips allows for treating sequential flips as equivalent to simultaneous flips, provided the events are independent. A critical distinction arises when interpreting the question regarding whether it asks for exactly two heads or at least two heads, which would yield different probabilities.

PREREQUISITES
  • Understanding of basic probability concepts
  • Familiarity with independent events in probability theory
  • Ability to construct probability trees or charts
  • Knowledge of combinatorial calculations (e.g., binomial coefficients)
NEXT STEPS
  • Study the binomial probability formula for calculating outcomes
  • Learn about independent and dependent events in probability
  • Explore the concept of cumulative probability for "at least" scenarios
  • Practice constructing probability trees for various coin flip scenarios
USEFUL FOR

Students, educators, and anyone interested in understanding probability theory, particularly in the context of independent events and coin flipping scenarios.

Punkyc7
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Question 1:
A coin is flipped 4 times. Find the probability that it lands heads twice.

Question 2:
Four coins are flipped simultaneously. Find the probability that exactly two of the land on heads


For the first one I made an H and T chart and got 6/16.

The second one I am thinking its the same thing.

My question is how is the second question any different from the first?
 
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Punkyc7 said:
Question 1:
A coin is flipped 4 times. Find the probability that it lands heads twice.

Question 2:
Four coins are flipped simultaneously. Find the probability that exactly two of the land on heads


For the first one I made an H and T chart and got 6/16.

The second one I am thinking its the same thing.

My question is how is the second question any different from the first?

Different questions, but same answer. You could get a different answer if the events were dependent on each other. However, tossing the coin doesn't affect the future coin tosses and you can treat it as tossing four coins at once. The fact that these are independent events is key.

__________

I noticed something about question 1. Is it asking for the probablility of exactly 2 heads or at least 2 heads? If at least 2 heads, then you would get a different answer.
 

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