Chapter 5 - Review - Case Study - The Case of the Body in the Bag - Page 320: 23

The age of the offender will be at least 18 because its conditional probability is 0.8796, which is maximum among all. The race of the offender will be white because its conditional probability is 0.8158, which is maximum among all, and the sex of the offender will be male because its conditional probability is 0.9088, which is maximum among all.

The best prediction of the variables on the basis of new information about the victim is given below. The offenders less than 18 from the provided table are 290 and the victims of at least 18 are 6398. The probability is calculated as follows: \[\begin{align} & \text{P}\left( \text{Offender is less than 18 / victim is at least 18} \right) \\ & =\frac{290}{6398} \\ & =0.0453 \\ \end{align}\] The offenders at least 18 from the provided table are 5628 and the victims of at least 18 are 6398. The probability is calculated as follows: \[\begin{align} & \text{P}\left( \text{Offender is at least 18 / victim is at least 18} \right) \\ & =\frac{5628}{6398} \\ & =0.8796 \\ \end{align}\] The offenders with age unknown from the provided table are 480 and the victims of at least 18 are 6398. The probability is calculated as follows: \[\begin{align} & \text{P}\left( \text{Age of offender is unknown / victim is at least 18} \right) \\ & =\frac{480}{6398} \\ & =0.0750 \\ \end{align}\] The white offenders from the provided table are 3026 and white victims are 3709. The probability is calculated as follows: \[\begin{align} & \text{P}\left( \text{Offender is white / victim is white} \right) \\ & =\frac{3026}{3709} \\ & =0.8158 \\ \end{align}\] The black offenders from the provided table are 573 and white victims are 3709. The probability is calculated as follows: \[\begin{align} & \text{P}\left( \text{Offender is black / victim is white} \right) \\ & =\frac{573}{3709} \\ & =0.1544 \\ \end{align}\] The other offenders from the provided table are 573 and white victims are 3709. The probability is calculated as follows: \[\begin{align} & \text{P}\left( \text{Offender is other / victim is white} \right) \\ & =\frac{53}{3709} \\ & =0.0142 \\ \end{align}\] The male offenders from the provided table are 1735 and female victims are 1909. The probability is calculated as follows: \[\begin{align} & \text{P}\left( \text{Offender is male / victim is female} \right) \\ & =\frac{1735}{1909} \\ & =0.9088 \\ \end{align}\] The female offenders from the provided table are 150 and female victims are 1909. The probability is calculated as follows: \[\begin{align} & \text{P}\left( \text{Offender is female / victim is female} \right) \\ & =\frac{150}{1909} \\ & =0.0785 \\ \end{align}\] The unknown offenders from the provided table are 24 and female victims are 1909. The probability is calculated as follows: \[\begin{align} & \text{P}\left( \text{Sex of offender is unknown / victim is female} \right) \\ & =\frac{24}{1909} \\ & =0.0125 \\ \end{align}\]