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

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In summary, the question is how to find the probability of getting 3 consecutive heads or more in 20 coin flips. The approach suggested is to calculate the number of possible outcomes, assuming the first 3 flips are heads and counting all other combinations. However, this approach does not account for cases where early flips were heads but not 3 consecutive. To get the exact answer, it is recommended to use software such as R or MATLAB or go to wolframalpha.com to check.
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:
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.

You omitted all cases where early flips were heads, but not 3 consecutive.

## 1. What is the probability of getting 3 heads or more in 20 coin flips?

The probability of getting 3 heads or more in 20 coin flips is approximately 0.498 or 49.8%. This means that in a large number of trials, about half of them will result in 3 or more heads.

## 2. How is the probability calculated for getting 3 heads or more in 20 coin flips?

The probability is calculated using the binomial distribution formula, which takes into account the number of trials (20 coin flips) and the probability of success (0.5 for a fair coin). The formula is P(x≥3) = 1 - binomcdf(20, 0.5, 2) where binomcdf is the cumulative binomial distribution function.

## 3. Is the probability of getting 3 heads or more in 20 coin flips affected by the order of the flips?

No, the probability remains the same regardless of the order of the flips. This is because each coin flip is independent and the probability of getting heads or tails does not change with each flip.

## 4. What is the likelihood of getting exactly 3 heads in 20 coin flips?

The likelihood of getting exactly 3 heads in 20 coin flips is approximately 0.206 or 20.6%. This can be calculated using the binomial distribution formula, P(x=3) = binompdf(20, 0.5, 3).

## 5. How does increasing the number of coin flips affect the probability of getting 3 heads or more?

As the number of coin flips increases, the probability of getting 3 heads or more also increases. This is because with more trials, the results tend to approach the expected probability of 0.5. For example, if we increase the number of coin flips to 100, the probability of getting 3 heads or more becomes approximately 0.999 or 99.9%.

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