Question

10 pennies fell on the floor. 2 of the pennies landed on heads. What is the theoretical probability of this happening?

Answer 1

The theoretical probability of this happening is 4.39%.

Explanation:

For each coin, there are only two possible outcomes. Either it lands on heads, or it lands on tails, the probability of a coin landing on heads is independent of other coins. 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.

10 coins:

This means that
`n = 10`

Supposedly fair:

This means that the probability of being heads or tails is equal. So
`p = 0.2`

10 pennies fell on the floor. 2 of the pennies landed on heads. What is the theoretical probability of this happening?

We have to find P(X = 2).

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

`P(X = 2) = C_(10,2).(0.5)^(2).(0.5)^(8) = 0.0439`

The theoretical probability of this happening is 4.39%.