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Concept

- There are two possible outcomes for each trial — success and failure.
- The trials are independent.
- The probability of success is the same on each trial.

If $p$ is the probability of success and $n$ is the number of trials needed to get a success, the probability of getting a success in $n$ trials is given by the formula below.

$P(X=n)=(1−p)_{n−1}p$

It is worth noting that this experiment satisfies the three conditions because the probability of landing on heads is $0.5$ for every trial. The following expression gives the probability of landing on heads after $n$ trials.

$P(X=n)P(X=n) =0.5_{n−1}0.5⇓=0.5_{n} $

The graph below displays the probabilities for values of $n$ from $1$ to $10.$ The value of $n=1$ indicates that the coin is flipped once before it lands on heads. The value of $n=2$ indicates that the coin lands on heads the second time it is flipped, and so on.
It should be noted that the probability of landing on heads after $n$ coin flips is equal to the probability of landing on tails after $n−1$ consecutive coin flips, then landing on heads on the next flip.

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