Question

An instructor who taught two sections of MTH132, with 20 and 30 students respectively. The instructor randomly select 15 students for a field trip. 1. What is the chance that exactly 10 of them are from the 2nd section?

2. What is the chance that at least 10 of them are from the 2nd section?

3. What is the chance that at least 10 of them are from the same section?

Answer 1

Number of students in section 1 = 20

Number of students in section 2 = 30

The 15 students for a field trip can be selected by the instructor in 50C15 ways.

1. Number of ways of selection if exactly 10 students are selected from the 2nd section = (30C10)*(20C5)

Chance that exactly 10 of them are from the 2nd section

= (30C10)*(20C5)/(50C15)

= 0.207

2. Chance that at least 10 of them are from the second section

= Chance that exactly 10 of them are from the 2nd section + Chance that exactly 11 of them are from the 2nd section + Chance that exactly 12 of them are from the 2nd section + Chance that exactly 13 of them are from the 2nd section + Chance that exactly 14 of them are from the 2nd section + Chance that exactly 15 of them are from the 2nd section

= (30C10)*(20C5)/(50C15) + (30C11)*(20C4)/(50C15) + (30C12)*(20C3)/(50C15) + (30C13)*(20C2)/(50C15) + (30C14)*(20C1)/(50C15) + (30C15)*(20C0)/(50C15)

= 0.207 + 0.118 + 0.044 + 0.010 + 0.001 + 0.000

= 0.38

3. Chance that at least 10 of them are from the same section

= Chance that at least 10 of them are from the 1st section + Chance that at least 10 of them are from the 2nd section

= Chance that exactly 10 of them are from the 1st section + Chance that exactly 11 of them are from the 1st section + Chance that exactly 12 of them are from the 1st section + Chance that exactly 13 of them are from the 1st section + Chance that exactly 14 of them are from the 1st section + Chance that exactly 15 of them are from the 1st section + Chance that at least 10 of them are from the 2nd section

= (20C10)*(30C5)/(50C15) + (20C11)*(30C4)/(50C15) + (20C12)*(30C3)/(50C15) + (20C13)*(30C2)/(50C15) + (20C14)*(30C1)/(50C15) + (20C15)*(30C0)/(50C15) + 0.38

= 0.01170 + 0.00204 + 0.00022 + 0.00001 + 0.516*10^-6 + 0.006*10^-6 + 0.38

= 0.39