Question

fifty percent of the people that get mail-order catalogs order something. find the probability that exactly tw0 of 10 people getting these catalogs will order something.

Answer 1

Given:

50% of the people that get mail-order catalogs order something.

Determine the probability that exactly 2 out of 10 people getting the catalogs will order something.


If the total number of people is 10, we can calculate the number of people who will order something from the catalogs:

10 * 0.50 = 5 people.

The probability that exactly two out of ten people will order something is:

2/5 = 0.4

Therefore, there is a 40% chance that the exact two people who received the catalogs will order something from it.

Answer 2

There is a 4.39% probability that exactly two of 10 people getting these catalogs will order something.

Explanation:

For each person that get mail-order catalogs, there are only two possible outcomes. Either they order something, or they do not. 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 = 10, p = 0.5`

Find the probability that exactly tw0 of 10 people getting these catalogs will order something.

This is 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`

There is a 4.39% probability that exactly two of 10 people getting these catalogs will order something.