Question

A coin is tossed 10 times. What is the probability of getting all tails? Express your answer as a simplified fraction or a decimal rounded to four decimal places.

Answer 1

The probability of getting all tails is
`(1)/(1024)`.

Explanation:

For each time the coin is tossed, there are only two possible outcomes. Either it is tails, or it is not. So 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 combinations 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:

A coin is tossed 10 times, which means that
`n = 10`

Outcomes of heads and tails are equally as likely, so
`p = (1)/(2)`

What is the probability of getting all tails?

This is
`P(X = 10)`

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

`P(X = 10) = C_(10,10).((1)/(2))^(10).(1-(1)/(2))^(0) = (1)/(2^(10)) = (1)/(1024)`

The probability of getting all tails is
`(1)/(1024)`.