Question

10- There are names for 30 people in a hat, 10 are students, 3 administrators and the rest are teachers. If you select 4 names at random without replacement, what is the probability that you get two students and two teachers?

Answer 1

Total number of names in the hat=30

Number of students=10

Number of teachers=17

Probability of student = 10/30

Probability of teacher = 17/30

Six orderings are possible for getting 2 students and 2 teachers. Let S denote student and T denote teacher.The orderings are

SSTT, STTS, STST, TSST, TSTS, TTSS

We select 4 names at random without replacement, probability that you get two students and two teachers is for one ordering is given by,

Since 6 orderings are possible, required probability,

$P=0.0372*6=0.2232$