Question

Four municipalities (denoted A, B, C and D) decided to award nine $1000 scholarships to college students who reside in either of them. The following table shows the distribution of candidates per municipality. Municipality # of candidates 12 from municipality A, 13 from B, 14 from C and 11 from D, Total 50 Scholarships are drawn (without replacement) at random from the 50 college students. What is the probability that two students from the municipality A and 3 from the municipality B receive a scholarship?

Answer 1

Given data:

Municipality A = 12

Municipality B = 13

Municipality C = 14

Municipality D = 11

Total students = 50

Number of people selected:

Municipality A = 2

Municipality B = 3

Total selected = 5

Number of ways of selecting 5 students from 50 students is given by:

Number of ways of selecting 2 students from Municipality A from 12 students from Municipality A is given by:

Number of ways of selecting 3 students from Municipality B from 13 students from Municipality B is given by:

So

Required Probability is given by:

So,

Answer is:

0.008909