Question

a random sample of 82 statistics student were asked about their latest test score pass or fail and rather they study for the test or not the following contingency table gives a two-way classification of their response

Answer 1

Given:

Sample size, n = 82

We have the repsonses on the table.

Suppose a student is randomly selected, let's determine the following probabilities.

Number that studied and pass = 22

Number of students that paased = 22 + 26 = 48

a) P(Did Study and Pass) =

`P=\frac{\text{Number that studied and pass}}{\text{Total number of students}}=(22)/(82)=0.268`

b) P(Did not Study and Fail):

Total number that failed = 10 + 24 = 34

Number that did not study and fail = 24

`P=\frac{Number\text{ that did not study and fail}}{Total\text{ number of students}}=(24)/(82)=0.293`

c) P(Pass or Did not Study):

`P=(26+22+24)/(82)=(72)/(82)=0.878`

d) P(Fail or did study):

`P=(10+24+22)/(82)=0.683`

e) P(Fail and Pass) = 0

This is zero since there is no inetrsection for students who fail and students who pass

ANSWER:

• P(Did Study and Pass) = 0.268

,

• P(Did not Study and Fail) = 0.293

,

• P(Pass or Did not Study) = 0.878

,

• P(Fail or did Study) = 0.683

,

• P(Fail and Pass) = 0