Question

4.2 question 15

The following table presents the number of reports of graffiti in each of New York's five boroughs over a one-year period. These reports were classified as being open, closed, or pending. A graffiti report is selected at random. Compute the following probabilities. Round final answer to four decimal places.(

Borough	Open Reports	Closed Reports	Pending Reports	Total
Bronx	1121	1622	80	2823
Brooklyn	1170	2706	48	3924
Manhattan	744	3380	25	4149
Queens	1353	2043	25	3421
Staten Island	83	118	0	201
Total	4471	9869	178	14518

a) The report is open and comes from Staten Island. The probability that the report is open and comes from Staten Island is___?

(b) The report is closed or comes from Bronx. The probability that the report is closed or comes from Bronx is__?

(c) The report comes from Manhattan. The probability that the report comes from Manhattan is __?

(d) The report that does not come from Manhattan. The probability that the report does not come from Manhattan is __?

(e) The report is closed. The probability that the report is closed is __?

(f) The report is from the Brooklyn or Queens. The probability that the report is from the Brooklyn or Queens is__?

Answer 1

a)

probability that the report is open and comes from Staten Island is=83/14518 =0.0057

b)

probability that the report is closed or comes from Bronx is=(9869+2823-1622)/14518 =0.7625

c)

probability that the report comes from Manhattan is =4149/14518 =0.2858

d)probability that the report does not come from Manhattan is =1-0.2858=0.7142

e)  probability that the report is closed is =9869/14518 =0.6798

f)  probability that the report is from the Brooklyn or Queens is =(3924+3421)/14518 =0.5059