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? (a) The probability that both will be hopelessly romantic is

0.0361.

(Round to four decimal places as needed.)

(b) The probability that at least one person is hopelessly romantic is

0.3439.

(Round to four decimal places as needed.)

a)

The probability that both will be hopelessly romantic is  

                                                             P(X = 2)   =  0.0361

b)

The probability that at least one person is hopelessly romantic is

               P( X>1) = 0.3439

Step-by-step explanation:

a)

Given data population proportion 'p' = 19% =0.19

                                                          q  = 1-p = 1- 0.19 =0.81

Given  two people are randomly selected

 Given n = 2

Let 'X' be the random variable in binomial distribution

The probability that both will be hopelessly romantic is

                     P(X = 2)   = 1 × 0.0361

The probability that both will be hopelessly romantic is  

                                                             P(X = 2)   =  0.0361

b)

The probability that at least one person is hopelessly romantic is

               P( X>1) = 1-P(x<1)

                            = 1 - ( p(x =0)

                            =

                           = 1 - (0.81)²

                           = 1 -0.6561

                           = 0.3439

The probability that at least one person is hopelessly romantic is

               P( X>1) = 0.3439

is there a picture

step-by-step explanation: