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ankoles [38]
2 years ago
10

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
SAT
1 answer:
mezya [45]2 years ago
4 0

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.

<h3>What is the binomial distribution formula?</h3>

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

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