Question

About 7% of the population of a large country is nervous around strangers. If two people are randomly selected, what is the probability both are nervous around strangers? What is the probability at least one is nervous around strangers? The probability that both will be nervous around strangers is . (Round to four decimal places as needed.) The probability that at least one person is nervous around strangers is . (Round to four decimal places as needed.)

Answer 1

Answer:

Probability both are nervous around strangers = 0.0049

Probability at least one is nervous around strangers = 0.1302

Step-by-step explanation:

Let probability a person selected in the population is nervous around strangers = P

                                        P = 7%

                                        P = $\frac{7}{100}$

                                        P = 0.07

Let probability a person selected in the population is not nervous around strangers = P'

                                         P' = 1 - P

                                         P' = 1 - 0.07

                                         P' = 0.93

(i) probability of the first person selected is nervous around strangers = P

   probability of the second person selected is nervous around strangers = P

   Probability both are nervous around strangers = (P × P)

                                         = 0.07 × 0.07

                                         = 0.0049

(ii) Probability at least one is nervous around strangers = ( probability the first person is nervous around strangers AND the second person is not nervous around strangers ) OR ( probability the second person is nervous around strangers AND the first person is not nervous around strangers)

This implies,

Probability at least one is nervous around strangers = (P × P') or (P × P')

                                        = (0.07 × 0.93) + (0.07 × 0.93)

                                        = 0.0651 + 0.0651

                                        = 0.1302