## Related questions with answers

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.

$\begin{array}{lrrrr} \hline & \text{Open} & \text{Closed} & \text{Pending} & \\ \text{Borough} & \text{Reports} & \text{Reports} & \text{Reports} & \text{Total}\\ \hline \text{Bronx} & 1,121 & 1,622 & 80 & 2,823\\ \text{Brooklyn} & 1,170 & 2,706 & 48 & 3,924\\ \text{Manhattan} & 744 & 3,380 & 25 & 4,149\\ \text{Queens} & 1,353 & 2,043 & 25 & 3,421\\ \text{Staten Island} & 83 & 118 & 0 & 201\\ \hline \text{Total} & 4,471 & 9,869 & 178 & 14,518\\ \end{array}$

A graffiti report is selected at random. Compute the following probabilities.

$\textbf{a.}\hspace{10pt}$ The report is open and comes from Brooklyn.

$\textbf{b.}\hspace{10pt}$ The report is closed or comes from Queens.

$\textbf{c.}\hspace{10pt}$ The report comes from Manhattan.

$\textbf{d.}\hspace{10pt}$ The report does not come from Manhattan.

$\textbf{e.}\hspace{10pt}$ The report is pending.

$\textbf{f.}\hspace{10pt}$ The report is from the Bronx or Staten Island.

Solution

Verified**(a)**

To determine the probability that a randomly selected report is open and comes from Brooklyn we will use this equation below.

$P(A)=\frac{\text{Number of open reports from Brooklyn}}{\text{Total number of graffiti reports}}$

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