Probability of At Least 1 Heads in 5 Coins Toss

  • Context: High School 
  • Thread starter Thread starter Jfontenot06
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Discussion Overview

The discussion revolves around calculating the probability of getting at least one head when flipping five coins. Participants explore different approaches to solving the problem, including hints and mathematical reasoning.

Discussion Character

  • Exploratory, Homework-related, Mathematical reasoning

Main Points Raised

  • One participant asks for the probability of at least one head in five coin flips.
  • Another participant prompts for thoughts on solving the problem and requests to show work before receiving help.
  • A hint is provided suggesting that the probability of at least one head can be calculated as 1 minus the probability of no heads.
  • One participant proposes that the probability of all five coins landing on heads is (1/2)^5 = 1/32, indicating a misunderstanding of the problem.
  • A participant corrects this by emphasizing the need to consider the probability of getting no heads instead.
  • Another participant suggests looking at the chances of none of the coins landing on heads as a different angle to approach the problem.
  • A participant shares a breakdown of outcomes for three coin tosses, inviting corrections and further discussion.

Areas of Agreement / Disagreement

Participants do not reach a consensus, as there are differing interpretations of how to approach the problem and some misunderstandings regarding the calculations involved.

Contextual Notes

Some assumptions about the independence of coin flips and the definitions of probability may not be fully articulated, leading to potential misunderstandings in the calculations presented.

Jfontenot06
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If you have five coins and you flip them what is the probability that at least one coin falls heads?
 
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Well, what are your thoughts about the problem? Do you have any idea on how you can solve this? You need to show your work before you get help.
 
Hint: prob at least 1 head = 1 - prob no heads. Try working from there.
 
Well what I was thinking is that the chances of a coin landing on heads is 1/2. Since there are five coins it should be (1/2)^5 = 1/32 :bugeye:
 
That would be the probability of all 5 coins landing on heads.

Look back at mathman's hint again, that is where you want to go with the problem.
 
Same hint, different angle:

What are the chances of throwing a set and having NONE turn up heads?
 
For one coin: 3 tosses

2 x 2 x 2

1st toss = happens 2 ways
2nd toss = happens 2 ways
3rd toss = happens 2 ways

s = { HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

Feel free to correct this. Cheers
 

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