Before that you said: 'What is the chance of getting 10 heads in 10 trials? We concur, that this is 0.5^10 = 1/1024.' > So adding a new toss does not increase the chance, it leaves it the same (2/2048 = 1/1024)! No, it's not even close it's much more subtle.Īnyway, I was with you almost to the end, then you lost me when you said: > you still make a similar mistake than your friend, only the other way round On the other hand, drawing graphs of this size will get very. bulky You will see, that this will NOT result in 50% for 1024 tosses, but less. You can go on creating graphs of result-chains and count success vs. 2048 (2^11) possible results for all trials! So adding a new toss does not increase the chance, it leaves it the same (2/2048 = 1/1024)! You will see that it results in 2 cases which are success in total (10 heads in a row) vs. What is the overal chance for 10 heads in 11 trials?ĭraw a graph with all results of consecutive results of events (aka. But, if we get a tails in the first trial, we still got 10 trials to complete the streak! So if the next toss is heads (which is 50%), we still got a chance of 1/1024 to complete the trial. If the first toss is heads, the next 9 tosses have to be heads again. What is the chance to get 10 heads in 11 trials? What is the chance of getting 10 heads in 10 trials? We concur, that this is 0.5^10 = 1/1024. As explained before: If you toss a coin and don't get 'success', you make a complete new experiment with n successes within m-1 trials! So a 'fail' affects the whole experiment! The second question looks only into results within a given number of trials. The first question just looks on the event, even if it states previous results of events. So stating ' If i have a streak of 10 heads in a row, what is the chance to get an 11th head with the next toss?' is a complete different question than ' What is the over all chance to get a streak of n (or more) 'successes' in a row in a test with m tries?' You still make a similar mistake than your friend, only the other way roundĮach toss (event) is independant of previous events and their results.

Coin flip simulator