Question

In: Math

6 a) You and your friend are in a class with 12 students. For a project,...

6 a) You and your friend are in a class with 12 students. For a project, the class is randomly divided into two equal groups. “Randomly” means all divisions are equally likely. What is the probability that you and your friend end up in the same group?

6 b) Revisit part a). Calculate the probability that you and your friend will end up in the same group if the class is divided into three equal groups instead.

Expert Solution

There is a total of 12 students with you and your friend in a class.

a) The class is randomly divided into two equal parts that are 6 and 6.

Assign a different number to each student from 1 to 12. number 1 to 6 go in one group and numbers 7 to 12 goes in another group.

All possible partitions are obtained with equal probability by a random assignment.

First, assign a random number to you and then your friend.

After assigning a number to you, there are 11 random numbers available for your friend and 5 of these will put him in the same group as you.

That is the available random numbers for your friend in one group are 5 and the total random numbers after assigning the number to you are 11, therefore the probability is 5/11

The probability that you are your friend end up in the same group is

b) Now the class is divided into three equal groups instead of 2.

That is the class is divided into groups of 4, 4 and 4

Assign a different number to each student from 1 to 12. number 1 to 4 go in first group, numbers 5 to 8 goes in second group and numbers 9 to 12 goes in the third group.

All possible partitions are obtained with equal probability by a random assignment.

First, assign a random number to you and then your friend.

After assigning a number to you, there are 11 random numbers available for your friend and 3 of these will put him in the same group as you.

That is the available random numbers for your friend in one group are 3 and the total random numbers after assigning the number to you are 11, therefore the probability is 3/11

The probability that you and your friend will end up in the same group if the class is divided into three equal groups instead of 2 is

milcah answered 1 year ago

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