Question 1117538: Hello, I have a question! I tried the first one on my own and I think it's correct.Any help is greatly appreciated! Thank you so much! It helps me out a lot!
It's a two part question:
I flip a coin 3 times and get all heads.
1. Does that mean the next has got to be tails? Why or why not. I said no, because the next time you flip, it could be heads again.
2. In the long run, what proportion of flips will up as heads? This is where I am stuck. Again any help is greatly appreciated and welcomed! Thank you so much!
Found 2 solutions by math_helper, solver91311:
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website! 1. You are correct. No matter how many heads in a row, on the next flip P(heads) = 50%, P(tails) = 50% (assuming a fair coin of course).
2. What do you think? If you flip a coin 10 times you might get 7 heads, 3 tails
but 1000 times you might get 4700 heads, 5300 tails, 1000000 times
. maybe 510000 heads and 490000 tails. Doesn't it seem likely that for a huge number of flips, the ratio of number of heads to number of flips will approach 1/2?
Check out this simulator. It lets you flip a coin virtually 100's of thousands of times (check the Session box to make the numbers tally just your session).
http://www.btwaters.com/probab/flip/coinmainD.html
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
Your answer to part 1 is absolutely correct. If you flip a (fair) coin 99 times and get a head each time, the probability of a tail on the 100 flip is still one-half, exactly what the probability was on each of the preceding flips.
With a fair coin, as in one that doesn't have a drop of solder on it to make one side a little heavier, the probability of a specific outcome, let's say a head, on any given trial is one-half. You have one outcome that you call a success out of two possible outcomes. Since either outcome is equally likely (c.f. "fair coin"), the long run expectation is getting a head half of the time and a tail the other half.
However, do not confuse the concept of "expected outcome" with "predicting a future outcome". Every trial is completely independent of any previous trial or trials.
John
My calculator said it, I believe it, that settles it
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