Mathematics: About 19% of the population of a large country is hopelessly romantic. If two people are randomly selected, what is the probability both are hopelessly romantic? What is the probability at least one is hopelessly romantic?

About 19% of the population of a large country

Ответ:

Thiskid100

20.01.2022

Mathematics

3.61% probability that both are hopelessly romantic.

34.39% probability at least one is hopelessly romantic

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they are hopelessly romantic, or they are not. The probability of a person being hopelessly romantic is independent from other people. 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.

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

And p is the probability of X happening.

19% of the population of a large country is hopelessly romantic.

This means that p = 0.19

Two people are randomly selected

This means that n = 2

What is the probability both are hopelessly romantic?

This is P(X = 2). So

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

$P(X = 2) = C_{2,2}.(0.19)^{2}.(0.81)^{0} = 0.0361$

3.61% probability that both are hopelessly romantic.

What is the probability at least one is hopelessly romantic?

$P(X \geq 1) = P(X = 1) + P(X = 2)$

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

$P(X = 1) = C_{2,1}.(0.19)^{1}.(0.81)^{1} = 0.3078$

$P(X = 2) = C_{2,2}.(0.19)^{2}.(0.81)^{0} = 0.0361$

$P(X \geq 1) = P(X = 1) + P(X = 2) = 0.3078 + 0.0361 = 0.3439$

34.39% probability at least one is hopelessly romantic

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Ответ:

jbarbie3

07.10.2022

Mathematics

Step-by-step explanation:

Order the values from least to greatest

55, 58, 62, 63, 68, 70, 71, 79, 81, 82

The median is the middle number in a set of data, but in the case where the amount of data is even, we find the average of the middle 2 numbers and count that as the median.

In this case, 68 and 70 are the middle 2 numbers

68 + 70 = 138 138 / 2 = 69

69 is the median for this set of data.

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About 19% of the population of a large country is hopelessly romantic. If two people are randomly selected, what is the probability both are hopelessly romantic? What is the probability at least one is hopelessly romantic?

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