Question

A random sample of 401 student were recent survey regarding their class standing freshmen software junior senior and their major type stem versus nonstem the following contingency table gives the 2 way classification of the response suppose one student is randomly selected from a group calculate the following probability

Answer 1

the Solution

`Pr(\text{STEM)}=(158)/(401)=0.394`
`Pr(\text{Sophomore)}=(87)/(401)=0.217`
`Pr(sophomore|Non-stem)=(68)/(401)=0.170`
`Pr(\text{sophomore and Non-stem)=}(87)/(401)*(243)/(401)=(21141)/(160801)=0.1315`

To ascertain whether Sophomore and Non-stem are dependent, we have to test the following:

`\begin{gathered} If\text{ Pr(sophomore or Non-stem) = Pr(sophomore and Non-stem),} \\ \text{then we conclude that both events are Independent,} \\ \text{otherwise, they are dependent.} \end{gathered}`
`\begin{gathered} Pr(\text{sophomore or Non-stem)=Pr(sophomore)+Pr(Non-stem)} \\ -Pr(\text{sophomore and Non-stem)} \end{gathered}`
`Pr(\text{Sophomore or Non-stem)=}(87)/(401)+(243)/(401)-((87)/(401)*(234)/(401))`
`=(330)/(401)-(21141)/(160801)=0.82294-0.13147=0.69147`

Cleary, we have that sophomore and non-stem events are dependent events since 0.69147 is not the same as 0.13147.