Question

A group of 60 students is randomly split into 3 classes of equal size. All partitions are equally likely. Jack and jill are two students belonging to that group. What is the probability that jack and jill will end up in the same class?

Answer 1

Answer:

⅓

Step-by-step explanation:

Total no. of favourable outcomes = 3

No. of possible outcomes = 1

$probability \: of \: the \: event \: = \frac{total \: no. \: of \: possible \: outcomes}{total \: no. \: of \: favourable \: outcomes}$

So,

Probability = ⅓

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Answer 2

Answer:

Assign a different number to each student from 1 to 60. Numbers 1 to 20 go in group 1, 21 to 40 go to group 2, 41 to 60 go to group 3.

All possible partitions are obtained with equal probability by a random assignment if these numbers, it doesn’t matter with which students we start, so we are free to start by assigning a random number to Jack and then we assign a random number to Jill. After Jack has been assigned a random number there are 59 random numbers available for Jill and 19 of these will put her in the same group as Jack. Therefore the probability is 19/59