Question

Guilty plea Not Guilty plea

Sentenced to prison 193 85
Not sentenced to prison 456 147

The above data was taken from a law journal article titled "Does it Pay to Plead Guilty?". If one of the subjects is randomly selected, find the probability of of selecting someone who was sentenced to prison or entered a plea of guilty.

Answer 1

0.8331 or 83.31%

Explanation:

According to the journal article:

`\begin{array}{ccc}Plea&Guilty&Not\ Guilty\\Sentenced&193&85\\Not \ Sentenced&456&147\end{array}`

There were 881 total subjects.

The number of subjects that were sentenced to prison or entered a plea of guilty is:

`N(S\ or\ G) = N(S) + N(G) - N(S\cap G)\\N(S\ or\ G) = (193+85) + (193+456) - 193\\N(S\ or\ G) = 734`

The probability of selecting someone who was sentenced to prison or entered a plea of guilty is:

`P = (734)/(881)=0.8331 =83.31\%`