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steve62388

macrumors 68040
Original poster
Apr 23, 2013
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Quick probability question please.

If I flip a coin 8 times, what is the likelihood of me correctly guessing the toss at least 6 times?
 
The chances are slim.

When using https://www.omnicalculator.com/statistics/probability and entering 50%* for both A & B:

  • at 6 events it is 1.5625%
  • at 7 events it is 0.78125%
  • at 8 events it is 0.390625%

Adding those 3 values together (at least 6 times = 6, 7 & 8 times) = 2.734375%

Back in high school, I would be able to do this manually and show the formula etc, but I'm a bit rusty now.

*To be picky, I did not calculate the chances that the coin would land on its curved edge/"thick" side - so the above value is a very good approximation.
 
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Back in high school, I would be able to do this manually and show the formula etc, but I'm a bit rusty now.
It’s a fairly simple one for independent events.

Probability raised to the number of events.

so just 0.5^6 then obviously + 0.5^7 + 0.5^8
 
Is that just adding up the chances of getting 6 out of 6, 7 out of 7 and 8 out of 8 correct? I’m not very good at this, so if you tell me it’s definitely the answer I’ll take your word for it. But it doesn’t sound like the right way to do it because I can get two out of the eight wrong.
 
Is that just adding up the chances of getting 6 out of 6, 7 out of 7 and 8 out of 8 correct? I’m not very good at this, so if you tell me it’s definitely the answer I’ll take your word for it. But it doesn’t sound like the right way to do it because I can get two out of the eight wrong.
Correct, your answer to how many out of x chances is as below.

There are 256 different permutations of Heads/Tails in 8 coin tosses.

Assuming you guess heads every time (assuming the coin is fair it doesn’t matter which you choose) there 28 combinations of getting 6 heads in 8

8 combinations of 7 in 8
1 combination of 8 in 8

(note: I use the words combination and permutation intentionally, the difference between them is key).

so getting at least 6 out of 8 you have 37 possibilities.

37/256 = 0.144 or 14.5%
 
Correct, your answer to how many out of x chances is as below.

There are 256 different permutations of Heads/Tails in 8 coin tosses.

Assuming you guess heads every time (assuming the coin is fair it doesn’t matter which you choose) there 28 combinations of getting 6 heads in 8

8 combinations of 7 in 8
1 combination of 8 in 8

(note: I use the words combination and permutation intentionally, the difference between them is key).

so getting at least 6 out of 8 you have 37 possibilities.

37/256 = 0.144 or 14.5%

Yeah, I thought that there might be a missing extra step somewhere (using Pascal's triangle).

It's been 16 years since studying this which was why I was a bit rusty.
 
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