Question

A fair coin is tossed 14 times. What is the probability of obtaining exactly 1 head? (Enter your answer as a reduced fraction or a decimal rounded to 4 places.)

Answer 1

0.0009 probability of obtaining exactly 1 head

Explanation:

For each toss, there are only two possible outcomes. Either it is a head, or it is not. The probability of a toss being a head is independent of any other toss. This means that we use the binomial probability distribution to solve this question.

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.

A fair coin is tossed 14 times.

Fair coin means that it is equally as likely to be heads or tails, so
`p = 0.5`

14 times means that
`n = 14`

What is the probability of obtaining exactly 1 head?

This is P(X = 1).

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

`P(X = 1) = C_(14,1).(0.5)^(1).(0.5)^(13) = 0.0009`

0.0009 probability of obtaining exactly 1 head