Question

Use the graph to solve this information

GENDER/ MAJOR	BIOLOGY (B)	NURSING (N)	TRANSPORTATION SYSTEMS (T)	OTHER (O)	TOTAL
MALE (M)	3	2	3	0	8
FEMALE (F)	8	22	0	2	32
TOTAL	11	24	3	2	40

Write all answers as a simplified fraction, decimal, or percentage.

If a student is randomly selected from our combined classes,

find the probability that the student is...

1. ...a nursing major.

P(N) = ________

2. ...not a nursing major.

P(N^C) = ________

3. ...male and a transportations systems major.

P(M and T) = ________

4. ...female or a biology major.

P(M or T) = ________

5. ...a female given that the student is a biology major.

P(F|B) = ________

6. ...a biology major given that the student is a female.

P(B|F) = ________

Circle the pairs of gender and major variables that are mutually exclusive?

• Male & Biology

• Male & Nursing

• Male & Transportation Systems

• Female & Biology

• Female & Nursing

• Female & Transportation Systems

Is being a female independent of being a nursing major? Explain your answer using the formula definition of independence.

________________________________________________________________________________________________________________________________________________________________

Answer 1

We would be looking at the first 4 parts here.

a) P(N) is computed here as:
P(N) = n(N) / n(Total) = 24/40 = 0.6

Therefore 0.6 is the probability here.

b) P(N^c) = 1 - P(N) = 1 - 0.6 = 0.4

Therefore 0.4 is the required prob. here.

c) P(M and T) = n(M and T) / n(Total) = 3/40 = 0.075

Therefore 0.075 is the required prob. here

d) P(M or T) = This is computed using the law of addition as:

P(M or T) = P(M) + P(T) - P(M and T)
= (8/40) + (3/40) - (3/40) = (8/40) = 0.2

Therefore 0.2 is the required prob. here