Is the probability of a random event influenced by previous random events?

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5outof4

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This is not a homework problem; I'm an old guy trying to analyze something correctly.

Suppose a coin is tossed 40 times and lands on heads 31 times. According to an online binomial probability calculator, the probability of this outcome is 0.00024869121262. Does this sound correct?

Now suppose the final 19 tosses had all landed on heads. Would it be valid to calculate the binomial probability of 19 out of 19, independent of the preceding 21 tosses, thereby arriving at a calculated probability of 0.00000190734863 for that string of 19 heads in a row? Or, would this constitute "cherry picking the data"?

I read somewhere that 5 out of 4 people have trouble with statistics, hence my username.
 
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Yes, 0.00024869121262 is correct.

0.00000190734863, is correct if you are asking what is the probability of getting 19 heads out of 19 tosses.

That answer will be larger if you want to know the probability that in a toss of 40 coins that somewhere there was 19 heads in a row.
 
5outof4 said:
This is not a homework problem; I'm an old guy trying to analyze something correctly.

Suppose a coin is tossed 40 times and lands on heads 31 times. According to an online binomial probability calculator, the probability of this outcome is 0.00024869121262. Does this sound correct?

Now suppose the final 19 tosses had all landed on heads. Would it be valid to calculate the binomial probability of 19 out of 19, independent of the preceding 21 tosses, thereby arriving at a calculated probability of 0.00000190734863 for that string of 19 heads in a row? Or, would this constitute "cherry picking the data"?

I read somewhere that 5 out of 4 people have trouble with statistics, hence my username.
Click to expand...
A few requirements for binomial. You've violated those 2 of you were to do that.
  1. Fixed number of trials: The number of trials must be fixed and known in advance.
  2. Independent trials: Each trial must be independent of the others, meaning that the outcome of one trial does not affect the outcome of any other trial.
 
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Steven G said:
Yes, 0.00024869121262 is correct.

0.00000190734863, is correct if you are asking what is the probability of getting 19 heads out of 19 tosses.

That answer will be larger if you want to know the probability that in a toss of 40 coins that somewhere there was 19 heads in a row.
Click to expand...

Thank you very much!

How would "the probability that in a toss of 40 coins that somewhere there was 19 heads in a row" be calculated?
 
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5outof4 said:
Thank you very much!

How would "the probability that in a toss of 40 coins that somewhere there was 19 heads in a row" be calculated?
Click to expand...
How many ways can you get 19 heads in a row in 40 tosses? This shouldn't be hard to determine.
Multiply that number by 0.00000190734863
 
5outof4 said:
Thank you very much!

How would "the probability that in a toss of 40 coins that somewhere there was 19 heads in a row" be calculated?
Click to expand...

There are 22 places a string of 19 heads can exist in 40 slots. If the other 21 slots can be heads or tails, then the probability is 11/262144.
 
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