Question

About ​% of the population of a large country is. If two people are randomly​ selected, what is the probability both are ​? what is the probability at least one is ​? assume the events are independent

Answer 1

Using the binomial distribution, it is found that there is a:

• 0.0036 = 0.36% probability that both are allergic to pollen.

• 0.1164 = 11.64% probability that at least one is allergic to pollen.

What is the binomial distribution formula?

The formula is:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

• x is the number of successes.

• n is the number of trials.

• p is the probability of a success on a single trial.

Researching the problem on the internet, it is found that:

• 6% of the population is allergic to pollen, hence p = 0.06.

• Two people are chosen at random, hence n = 2.

The probability that both are allergic is P(X = 2), hence:

P(X = 2) = 0.06^2 = 0.0036.

0.0036 = 0.36% probability that both are allergic to pollen.

The probability of at least one is:

P(X >= 1) = 1 - P(X = 0) = 1 - 0.94^2 = 1 - 0.8836 = 0.1164.

0.1164 = 11.64% probability that at least one is allergic to pollen.

More can be learned about the binomial distribution at brainly.com/question/24863377