Question

2.1.40: The police records of a city contain the following statistics on offenses for the month of May: 430 assaults, 146 robberies, and 131 drug sales. The records also show that 26 people were involved in both assault and robbery and that 33 people were involved in both assault and drug sales. What is the greatest possible number of offenders for May who satisfy these statistics

Answer 1

648

Explanation:

Number of Assaults, n(A)=430

Number of Robberies, n(R)=146

Number of Drug Sales Offenses, n(D)=131

Number involved in both assault and robbery=
`n(A\cap R)=26`

Number involved in both assault and drug sales=
`n(A\cap D)=33`

Therefore, to find the greatest possible number of offenders for May who satisfy these statistics, we remove the number of those who were involved in more than one crime.

This gives us:

`=n(A)+n(R)+n(D)-n(A\cap R)-n(A\cap D)\\=430+146+131-26-33\\=648`

The greatest possible numbers of offenders in May is 648.