# Probability of getting 3 heads or more in 20 coin flips

• I
hey folks,

My question is how to find probability of getting 3 CONSECUTIVE heads or more in 20 coin flips, what are the odds

I have an approach which I need to verify and please clarify in case of missing points.

No. of possible outcomes = 2 ^ 20

first I assume that first 3 outcomes are heads , all other 17 combinations of coins are to be counted, so there are 2 ^ 17 .
then I assume first outcome is tail, and 2nd,3rd,4th outcomes are heads, all other 16 combinations of coins are to be counted , so there are 2^16
then I assume first outcome AND second outcome both are tail, and 3rd,4th,5th outcomes are heads , other 15 combinations are 2^15
then I assume first outcome , second outcome AND third outcome all are tail, and 4th,5th,6th outcomes are heads , other 14 combinations are 2^14

and so on until
1st to 17th outcome are all tail , and 18th,19th,20th are heads, possibility is 2^0 which is 1

so the answer is 2^17 + 2^16 + 2^15 + ...... 2^0 which gives 262143 , with a probability of 0.25

are there any misleading overlapping cases?

and please check R software or matlab or others to get the exact answer

Last edited:

## Answers and Replies

EnumaElish
Science Advisor
Homework Helper
hey folks, ...
and please check R software or matlab or others to get the exact answer
You can go to wolframalpha.com and check it yourself.

• Fady
mathman
Science Advisor
You omitted all cases where early flips were heads, but not 3 consecutive.

• EnumaElish and Fady