Question

There are 200 graduate students at a California State University; of whom 110 are female (F) and 125 are international students (I). 70 are female and international students. 1) List the probability distribution table. 2) Are the variables “gender of students” and “origin of students” independent? Show your work. 3) What is the probability that the student is international given male? 4) What is the probability that the student is international or female? 5) We select at random two different students. What is the probability that the first student and the second student are both international?

Answer 1

	female	male	total
international	70	55	125
domestic	40	35	75
total	110	90	200

1) dividing each value in table by 200 ; below is probability distribution table

	female	male	total
international	0.35	0.275	0.625
domestic	0.2	0.175	0.375
total	0.55	0.45	1

2)

here as P(female and international)=0.35 ; while P(female)*P(international)=0.55*0.625=0.34375

as they both are not equal' therefeore they are nt independent

3)

probability that the student is international given male =0.275/0.45=0.6111

4)

probability that the student is international or female =0.35+0.2+0.275 =0.825

5)

probability that the first student and the second student are both international=(125/200)*(124/199)

=0.3894