Question

Crime data from the U.S. Federal Bureau of Investigation for the years 2012 and 2013 are given in the table below.

Year	Murder &       non-negligent manslaughter	Rape	Robbery	Aggravated assault	Burglary	Larceny-theft	Motor vehicle theft	Total
2012	14, 856	85, 141	355, 051	762, 009	2, 109, 932	6, 168, 874	723, 186	10, 219, 049
2013	14, 196	79, 770	345, 031	724, 149	1, 928, 465	6, 004, 453	699 ,594	9, 795 ,658
Total	29, 052	164, 911	700, 082	1, 486, 158	4 038, ,397	12, 173, ,327	1, 422 780	20, 014, 707

What is the probability that a randomly selected crime was murder & non- negligent manslaughter or aggravated assault for these two years?

Answer 1

we know that probability is defined as the ratio of favourable outcome to the total outcome

Probability = (favourable outcome)/(total outcome)

In this case, total outcome = 20,014,707

and favourable outcome = number of crimes(murder and non-negligent manslaughter)+number of crimes(aggravated assault)

so, favourable outcome = 29,052 + 1,486,158 = 1,515,210

Setting the value of favourable outcome and total outcome in the probability formula

we get  

Probability = (favourable outcome)/(total outcome) = (1,515,210)/(20,014,707) = 0.0757 (rounded to 4 decimal figures)