Question

If you flip a fair coin 777 times, what is the probability that you will get exactly 222 tails?

Answer 1

There is a less than 16.41% probability that you will get exactly 2 tails.

Explanation:

For each time you flip a coin, there are only two possible outcomes. Either it is heads, or it is tails. This means that we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

In which
`C_(n,x)` is the number of different combinatios of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

And p is the probability of X happening.

In this problem we have that:

`n = 7, p = 0.5`

What is the probability that you will get exactly 2 tails?

This is P(X = 2).

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

`P(X = 2) = C_(7,2).(0.5)^(2).(0.5)^(5) = 0.1641`

There is a less than 16.41% probability that you will get exactly 2 tails.