Question

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A total of 150 crimes were reported by the sheriff last year. Of the 150 crimes,...

A total of 150 crimes were reported by the sheriff last year. Of the 150 crimes, 39 were committed by criminals under 20 years of age, 36 were committed by criminals over 40 and 82 were violent crimes. There were 27 violent crimes under the age of 20 and 14 violent criminals over the age of 40.

Type of Crime	Under 20	20-40	Over 40	Total
Violent	27	41	14	82
Non Violent	12	34	22	68
Total	39	75	36	150

What is the probability that at least one out of four crimes is nonviolent? Please show work so I can understand how to get the answer

Expert Solution

n : Number of crimes = 4

Probability that a crime is nonviolent = Number of crimes that are violent / Total number of crimes

From the given table,

Number of crimes that are violent = 82

Total number of crimes = 150

Probability that a crime is nonviolent = Number of crimes that are nonviolent / Total number of crimes = 68/150=34/75

Probability that a crime is violent = 1-Probability that a crime is nonviolent = 1-34/75 = 41/75

Probability that at least one out of four crimes is nonviolent = 1 - Probability that none of the 4 crimes are nonviolent

Probability that none of the 4 crimes are nonviolent = Probability that all 4 crimes are violent

Probability that all 4 crimes are violent

= Probability that 1st crime is violent x probability that 2nd crime is violent x probability that 3rd crime is violent x probability 4th crime is violent

= (41/75)*(41/75)*(41/75)*(41/75) = 0.089308002

Probability that none of the 4 crimes are nonviolent = Probability that all 4 crimes are violent = 0.089308002

Probability that at least one out of four crimes is nonviolent

= 1 - Probability that none of the 4 crimes are nonviolent = 1-0.089308002 = 0.910691998

Probability that at least one out of four crimes is nonviolent = 0.910691998

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