# Sample Question: Probability

The following table gives the number of Property Crimes by category of crime and geographical region.

East South Midwest West Totals

Burglary 75 128 29 52 284

Motor Vehicle Theft 233 514 104 251 1102

Larceny 100 326 65 99 590

Totals 408 968 198 402 1976

(A) Referring to the above table, if a property crime is chosen at random, what is the probability that it is either from the South or from the Midwest?

(B) Referring to the above table, given that the crime is from the East, what is the probability that it is for a Motor Vehicle Theft?

(C) Referring to the above table, if a crime is chosen at random then what is the probability that it is a burglary?

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#### Solution Preview

We have total population of N. Out of these N objects, n have property x.

The probability to choose in random one object of property x out of the entire sample is P(n,N) = n/N

(A)

There are total of N=1976 property crimes nation wide. This is our population

There were n=198 property crimes in the ...

#### Solution Summary

The solution provides an answer to the probability sample question.

Three questions on probability

1) Researchers at a pharmaceutical company have found that the effective time duration of a safe dosage of a pain relief drug is normally distributed with mean 2 hours and standard deviation 0.3 hour. For a patient selected at random:

a) What is the probability that the drug will be effective for 2 hours or less?

b) 1 hour or less?

c) 3 hours or more?

2) Life span for red foxes follow an approximately normal distribution with mean 7 years and standard deviation 3.5 years.

a) Find the probability that a red fox chosen at random will live at least 10 years.

b) Find the probability that a random sample of 4 red foxes will have a sample mean life span of over 10 years.

3) Margot has found that the mean time to run a job at the college copy center is 12.6 minutes with standard deviation 10 minutes. She selects a random sample of 64 jobs.

a) What is the probability that the sample mean copying time is between 14 and 15 minutes?

b) What is the probability that the sample mean copying time for this sample is between 10 and 12 minutes?