Question

A teacher assigns a group of 30 students into 3 groups of 10. The way the assignment process works is as follows: the teacher first randomly picks 10 students from the class and assigns them to group 1; from the remaining group of students that have not been assigned, the teacher randomly picks 10 more and assigns them to group 2; finally, the remaining students not yet picked are all assigned to group 3. Henry and Marcel are friends and desperately want to be in the same group. To improve their chances, they quickly hide behind a cabinet, unnoticed, just before the teacher starts picking students. Immediately after the teacher has picked the 12th student, Henry quietly returns to his seat. Immediately after the teacher has picked the 16th student Marcel quietly returns to his seat. What is the probability that Henry and Marcel will be selected for the same group, and did they in fact improve their odds compared to simply staying in their seats the entire time?

Answer 1

sol:

answer:-

Given That:-

A teacher assigns a group of 30 students into 3 groups of 10. The way the assignment process works is as follows: the teacher first randomly picks 10 students from the class and assigns them to group 1; from the remaining group of students that have not been assigned, the teacher randomly picks 10 more and assigns them to group 2; finally, the remaining students not yet picked are all assigned to group 3.

Given,

What is the probability that henry and naral will be selected for the same group, and did they in fact improve their odds compared to simply staying in their seats the entire time.

Henry entered at his seat after 12th selection

Marcel entered at his seat after 16th selection

P(Henry and Marcel get selected in group 2) = 8/18 * 4/14

i.e,

Number of places remaining after entrance in group 2 / Total number of students unassigned

= 8/63

Because both are independent probabilities

P(Henry and Marcel get selected in group 3) =  

= (10*10) / (18 * 14)

= 25/63

P(Henry and Marcel get selected in some group) = P*

= 8/63 + 25/63

= 33/63

= 11/21

P(Henry and Marcel get selected in same group when they were present since start)

for each group

= 10/30 * 10/30 * 3

= 1/3

= p

P(Henry and Marcel after arrangement of 12th and 16th) > P(Henry and Marcel without arrangement)

P* > p

Thus, they both improves their chances to be selected in the same group than the sinply staying in their seats.

P(Henry and Marcel get selected in the same group) = 11/21

yes, Henry and Marcel improved their chances of selection into the same group by hiding behind than sitting entire time.

***Please Upvote......Its really usefull to us...If any querry comment below...I will resolve ASAP....Thank You....