Question

suppose the probability of someone having a reaction to a medication is 0.025 what is the probability of two out of tree people having a reaction?

Answer 1

0.0018 = 0.18% probability of two out of tree people having a reaction.

Explanation:

For each person, there are only two possible outcomes. Either they have a reaction, or they do not. The probability of a person having a reaction is independent of any other person. This means that the binomial probability distribution is used 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.

The probability of someone having a reaction to a medication is 0.025.

This means that
`p = 0.025`

What is the probability of two out of tree people having a reaction?

This is
`P(X = 2)` when
`n = 3`. So

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

`P(X = 2) = C_(3,2).(0.025)^(2).(0.975)^(1) = 0.0018`

0.0018 = 0.18% probability of two out of tree people having a reaction.