Question

(1-6) 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.

Borough	Open Report	Closed Report	Pending Report	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

Compute the following probabilities:

1. Find the probability a random report is open and comes from Brooklyn.

2. Find the probability a random report comes from Manhattan.

3. Find the probability a random report is not from Queens.

4.Given a report is from Staten Island, what is the probability it is closed.

5. Find the probability a random report comes from Brooklyn or is open.

6. Find the probability a report is from Manhattan, given it is pending.

Answer 1

1)

The required probability = 1170/14518 = 0.0806

2)

The required probability = 4149/14518 = 0.2858

3)

The required probability = 1 - (3421/14518) = 0.7644

4)

The required probability = 118/201 = 0.5871

5)

The required probability = P(Brooklyn) + P(Open) - P(Brooklyn and Open)

= (3924 + 4471 - 1170)/14518 = 0.4977

6)

The required probability = 25/178 = 0.1404