Question

The following chart shows the number of customer complaints from three regions of an organization for two separate years. 2018 2017 Northeast region 6,493 3,401 Southeast region 732 2,513 Central region 3,706 1,082 • Find the probability for each question. (75 words, or 1 paragraph)

o What is the probability that a complaint was from the Southeast region, given it was in 2017? o What is the probability that a complaint was from the Central region, given it was in 2018? o What is the probability that a given complaint did not occur in 2018 and was not from the Southeast region? o What is the probability that two complaints chosen at random were both from the Northeast region?

Answer 1

(a)

Given chart:

	2018	2017	Total
Northeast region	6493	3401	9894
Southeast region	732	2513	3245
Central region	3706	1082	4788
Total	10931	6996	17927

Question:

What is the probability that a complaint was from the Southeast region, given it was in 2017?

Answer:
P(Southeast region/ 2017) = P(Southeast region AND 2017) / P(2017)

                                  = 2513/6996

                                    = 0.3592

So,

Answer is:

0.3592

(b)

Question:

What is the probability that a complaint was from the Central region, given it was in 2018?

P(Central region/ 2018) = P(Central region AND 2018) / P(2018)

                                 = 3706/10931

                                 = 0.3390

So,

Answer is:

0.3390

(c)

Question:

What is the probability that a given complaint did not occur in 2018 and was not from the Southeast region?

P(NOT 2018 AND NOT Southeast region) = P(2017 AND (Northeast region OR Central region ))

                                                            = (3401 + 1082)/17927

                                                               = 0.2501

So,

Answer is:

0.2501

(d)

Question:

What is the probability that two complaints chosen at random were both from the Northeast region

P(both from the Northeast region) = (9894/17927)²

                                              = 0.5519²

                                           = 0.3046

So,

Answer is:

0.3046