Question

The data in the following table shows the outcomes of guilty and not-guilty pleas in 1060 criminal court cases. Complete parts (a) and (b) below. Sent to prison Not sent to prison Guilty plea 398 582 Not-guilty plea 69 11 a. What is the probability that a randomly selected defendant either pled guilty or was sent to prison? .99 (Round to three decimal places as needed.) b. What is the probability that a randomly selected defendent either pled not guilty or was not sent to prison? (Round to three decimal places as needed.)

Answer 1

$=p(plead \;guilty)=\frac{398+582}{1060}=\frac{980}{1060}=0.924$

$=p(prisoners)=\frac{398+69}{1060}=\frac{467}{1060}=0.440$

$p(guilty\cap sent\;to\;prison)=\frac{398}{1060}=0.375$$probability\;that\;a\;randomly\;selected\;defendent\;either\;pled\;guilty\;or\;was\;sent\;to\;prison=$

$p((pled\; guilty)\cup (sent\;to\;prison))=p(pled\;guilty)+p(sent\;to\;prison)-p(guilty\cap sent\;to\;prison)$

$=0.924+0.440-0.375$

$=1.364-0.375$

  $=0.989$

$b)probability\;of\;defendents\;not\;plead\;guilty\;\;p(not\;guilty)=\frac{69+11}{1060}=\frac{80}{1060}=0.075$

$probability\;of\;defendents\;not\;sent\;to\;prison\;\;p(not\;sent\;to\;prison)=\frac{582+11}{1060}=\frac{593}{1060}=0.559$$probability\;of\;defendents\;pled\;no\;guilty\;and\;not\;sent\;to\;prison\;\;p(not\;guilty\cap not\;sent\;to\;prison)=\frac{11}{1060}=0.010$

$p(pled\;not\;guilty\cup not\;sent\;to\;prison)=p(not guilty)+p(not\;sent\;to\;prison)-p(not\;guilty\cap not sent \;to\; prison)$

  $=0.075+0.559-0.010$

$=0.634-0.010$

$=0.624$