Popular streak (run) questions and answers.
All questions have p(Heads) and p(Tails) = 1/2 (50%)
1. Question: Probability run of at least 2 in 4 trials? Answer: 0.50
(1/2 or 50%)
2. Question: Probability run of at least 5 in 20 trials? Answer: 0.2498703
(32751/131072)
3. Question: Probability NO run of at least 5 in 20 trials? Answer: 0.75012970
(98321/131072)
4. Question: Probability run of at least 5 in 100 trials? Answer: 0.8101096
(64183494979494598846972364275/79228162514264337593543950336)
5. Question: Probability NO run of at least 5 in 100 trials? Answer: 0.1898904
(15044667534769738746571586061/79228162514264337593543950336)
6. Question: Probability run of at least 7 in 100 trials? Answer: 0.3175204
(6289139215543317778531752497/19807040628566084398385987584)
7. Question: Probability any run (Heads or Tails) of at least 3 in 9 trials? Answer: 0.78515625
(201/256)
run/trials probability data results using Fibonacci numbers. (R code) p(success) = 1/2.
runTrialsFib(2,2) means 'at least' a run of 2 in 2 trials. Trials are from 2 to 50 for run of length 2.
runTrialsFib(3,5) means 'at least' a run of 3 in 5 trials. Trials are from 3 to 100 for run of length 3.
Trials are from 4 to 200 for run of length 4.
Trials are from 5 to 200 for run of length 5.
run,Trials data (using Fibonacci numbers) for p(success)=1/2.
(2,8) means a run of at least 2 in 8 trials.
Average number of trials to see a run of at least 2 is 6 (for p=1/2).
Max Trials=50. Table scrolls.
run,Trials data (using Fibonacci numbers) for p(success)=1/2.
(3,10) means a run of at least 3 in 10 trials.
Average number of trials to see a run of at least 3 is 14 (for p=1/2).
Max Trials=100. Table scrolls.
run,Trials data (using Fibonacci numbers) for p(success)=1/2.
(4,10) means a run of at least 4 in 10 trials.
Average number of trials to see a run of at least 4 is 30 (for p=1/2).
Max Trials=200. Table scrolls.
run,Trials data (using Fibonacci numbers) for p(success)=1/2.
(5,10) means a run of at least 5 in 10 trials.
Average number of trials to see a run of at least 5 is 62 (for p=1/2).
Max Trials=200. Table scrolls.