Probability of Strikes and Crime Reporting

This document discusses the probability of strikes and crime reporting in various scenarios. It includes calculations for the probability of both groups striking, neither group striking, one group striking and the other not, and more. It also explains the concept of mutually exclusive events. Additionally, it provides calculations for the probability of the Russian wheat harvest being adequate and the probability of the United States having to sell more than 20 million metric tons to Russia. Lastly, it presents crime figures and calculates the probability of a crime being reported, given that an assault occurs, a nonreported crime being either a robbery or an assault, a crime being a rape and reported, and the probability of a crime being reported or being a robbery.

Problems
7.2 David Morgan, the city manager of Yukon, Oklahoma, must negotiate new
contracts with both the firefighters and the police officers. He plans to offer both
groups a 7% wage increase and hold firm. Mr. Morgan feels that there is one
chance in three that the firefighters will strike and one chance in seven that the
police will strike. Assume that the events are independent.
a. What is the probability that both will strike?
P(Both will strike) = P(Firefighters will strike)*P(Police officers will strike)
= (1/3)*(1/7) = 1/21
b. What is the probability that neither the police nor the firefighters will strike?
P(Neither will strike) = P(Firefighters will not strike)*P(Police officers will not strike)
= (2/3)*(6/7) = 4/7
c. What is the probability that the police will strike and the firefighters will not?
P(police will strike and the firefighters will not)
= P(police will strike)*P(Firefighters will not strike)
=(1/7)*(2/3) = 2/21
d. What is the probability that the firefighters will strike and the police will not?
P(firefighters will strike and the police will not)
= P(firefighters will strike)*P(police will not strike)
=(1/3)*(6/7) = 2/7
7.4 In your own words, explain what mutually exclusive events are.

Mutually exclusive events are two events where there is no probability of two ever occurring at the
same time. A good example is in a coin toss. There isn’t a possibility of getting both heads and tails at
the same time.
7.6 The National Crop Reporting Service receives the accompanying information from the Central
Intelligence Agency (CIA) on the Russian wheat harvest.
Russian demand for wheat is approximately 210 million metric tons.
(a) What is the probability that the harvest will be adequate?
= (0.15+0.07) / 2
= 0.11
= 11%
(b) If U.S. exports make up the difference, what is the probability that the United
States will have to sell more than 20 million metric tons to the Russians?
= 0.05+0.15+0.23
= 0.43
= 43%
Millions of Metric Tons Probability
Less than 170 .05
170–180 .15
180–190 .23
190–200 .31
200–210 .15
210–220 .07
More than 220 .04
7.8 From a survey of the households in Grayson, Missouri, the crime figures shown
in the accompanying table were estimated.
Crime Number Reported Number Not Reported Total
Murder 12 12 24
Robbery 145 105 250
Assault 85 177 262

Rape 12 60 72
Auto theft 314 62 376
Total 568 416 984
(a) What is the probability that a crime is reported?
= 568/984
=0.58
=58%
(b) What is the probability that a crime is reported, given that an assault occurs?
= 85/262
= 0.32
= 32%
(c) What is the probability that a nonreported crime is either a robbery or an
assault?
= (105/250) * (177/262)
= 0.42 * 0.68
= 0.29
= 29%
(c) What is the probability that a crime is a rape and that it is reported?
= (72/984) * (568/984)
= 0.07 * 0.58
= 0.04
= 4%
(e) What is the probability that a crime is reported or that the crime is a robbery?
= (568/984) + (250 / 984)
= 0.58 + 0.25
= 0.83
= 83%