Question

Giving a test to a group of students, the grades and gender are summarized below

	A	B	C	Total
Male	2	3	5	10
Female	16	9	8	33
Total	18	12	13	43

If one student is chosen at random,

Find the probability that the student was female OR got an "B". Round the solution to three decimal place

B)

A random sample of 116 statistics students were asked about thier latest test score (pass or fail) and whether they studied for the test or not. The following contingency table gives the two-way classification of their responses.

	Pass	Fail
Did Study	32	14
Did Not Study	34	36

Suppose one student is randomly selected from the group. Calculate the following probabilities.

Round solutions to three decimal places, if necessary.

P(P(Did Study and Pass)=)=

P(P(Did Not Study and Fail)=)=

P(P(Pass or Did Not Study)=)=

P(P(Fail or Did Study)=)=

P(P(Fail and Pass)=)=

P(P(Pass or Fail)=)=

C)

A random sample of 403 students were recent surveyed regarding their class standing (freshman, sophomore, junior, senior) and their major type (STEM vs. Non-STEM). The following contingency table gives the two-way classification of the responses.

	Freshman	Sophomore	Junior	Senior
STEM	16	83	59	22
Non-STEM	27	48	62	86

Suppose one student is randomly selected from the group. Calculate the following probabilities.

Round solutions to three decimal places, if necessary.

P(P(STEM)=)=

P(P(Sophomore)=)=

P(P(Sophomore | Non-STEM)=)=

P(P(Sophmore and Non-STEM)=)=

Are the events "Sophomore" and "Non-STEM" indpendent or dependent? Select an answer Independent Dependent

P(P(Sophmore or Non-STEM)=)=

D) Use the given information to determine the probabilities below.

P(A)=0.33P(A)=0.33        P(B)=0.41P(B)=0.41        P(B∣A)=0.14P(B∣A)=0.14

Round solutions to three decimal places, if necessary.

If AA and BB are assumed to be dependent events,

P(AP(A and B)=B)=

If AA and BB are assumed to be independent events,

P(AP(A and B)=B)=

If AA and BB are assumed to be dependent and mutually non-exclusive events,

P(AP(A or B)=B)=

If AA and BB are assumed to be dependent and mutually exclusive events,

P(AP(A or B)=B)=

E) A sample of 450 deer in a forest are tested for particular a disease. It is found that 40 of them test positive for the disease. Round solutions to three decimal places, if necessary.

The empirical probability that a randomly chosen deer will test positive is:

P(P(Test Positive)=)=  

The empirical probability that a randomly chosen deer will test negative is:

P(P(Test Negative)=)=  

Answer 1

We would be looking at the first 4 parts here as:

P( female or got a B)

= n(female or B) / n(Total)

= (33 + 3) / 43

= 36/43

= 0.837

Therefore 0.837 is the required probability here.

The probability here are computed as:

-- P(did study and pass)
= n(did study and pass) / n(Total)
= 32/116
= 0.276

Therefore 0.276 is the required probability here.

-- P(did not study and fail)
= n(did not study and fail) / n(Total)
= 36/116
= 0.310

Therefore 0.310 is the required probability here.

-- P( Pass or did not study )
= n(Pass or did not study ) / n(Total)
= (116 - 14)/116
= 102/116
= 0.879

Therefore 0.879 is the required probability here.

-- P(fail or did study)
= (116 - 34)/116
= 0.707

Therefore 0.707 is the required probability here.

-- P(fail and pass) = 0 as both pail and pass cannot happen together here.

-- P(Pass or fail) = 1 as there are only 2 possibilities pass or fail.