Question

Lorelei tosses a coin 4 times. What is the probability of tossing four heads? Express as a percent. Round to the nearest tenth if necessary.

Answer 1

6.2%

Explanation:

For each time the coin is tossed, there are only two possible outcomes. Either it is heads, or it is not. The probability of a toss resulting in heads is independent of other tosses. So 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.

Fair coin:

Equally as likely to be heads or tails, so
`p = 0.5`

Lorelei tosses a coin 4 times.

This means that
`n = 4`.

What is the probability of tossing four heads?

This is P(X = 4).

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

`P(X = 4) = C_(4,4).(0.5)^(4).(0.5)^(0) = 0.062`

0.062 = 6.2% probability of tossing four heads