Reference no: EM132402404

Kenan is investigating reports of graffiti in the different boroughs of New York City. Some of the reports are classified as open, others as closed, and others as pending. Each report can only be filed in one borough and can only have one classification at a time. Of all of the reports, 28.6% were filed in Manhattan, 27% were filed in Brooklyn, and 23.6% were filed in Queens. Roughly 30.8% of the reports are open, 68% of the reports are closed, and the rest are pending. Kenan finds that the probability that a report is pending or it's in Manhattan is 0.296 while the probability that a report is closed and filed in Queens is 0.141.

Define the following events:

M = the report is filed in Manhattan O = the report is open

B = the report is filed in Brooklyn      C = the report is closed

Q = the report is filed in Queens      P = the report is pending

a.  Complete the summary below.

p(M) =       p(O) =  

p(B) =       p(C) =  

p(Q) =       p(P) =  

p(P or M) =       p(C and Q) =  

Use an appropriate formula to determine each of the following events. Give your answers to the nearest thousandth (for example, write 0.3 as 0.300).

b. p(B^C) =  

c. p(M and B) =  

d. p(M or B) =  

e. p(P and M) =  

f. p(C or Q)