Math CentralQuandaries & Queries


Question from Aishwarya, a student:

A red, a blue and a green die are all thrown at the same time. Display all the possible outcomes in a suitable way. Find the probability of obtaining:-
1. A total of 18 on the three dice
2. a total of 4 on the three dice
3. a total of 10 on the three dice
4. a total of 15 on the three dice
5. a total of 7 on the three dice
6. the same number on each die..

Please, please help me...


This will be a longish list; there are 6x6x6 = 216 outcomes. I would suggest getting narrow-lined paper or squared paper with at last 36 rows on the page, and writing the possibilities systematically in six columns, using three colors of pen. Do note that (eg) 123, 213, 231, 321, 312, 132 are all different, as are 556, 565, 655.

Once you've done this, you can just count the ways of getting each of the outcomes below, but it would be good to look for a pattern!

For instance, how many ways are there to get a total of 6?
With two ones: 114,141,411
With a 1 and a 2: 123, 213, 231, 321, 312, 132
With no 1: 222 (only)

Total, ten ways in 216, so P(R+G+B=6) = 10/216 = 5/108.

Good Hunting!

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