I’m trying to teach myself some probability. I’m solving some problems involving non-transitive dice. While I feel I understand most of the material, I don’t conceptually understand the following:
Suppose you have a single dice D with the following sides: 3 3 3 3 3 6
I’m trying to determine the probability of the sums when rolling two D dices.
Obviously, the only possible sums are: 6, 9, and 12.
It’s apparent to me that:
P(sum equals 6) = 5/6 * 5/6 = 25/36
P(sum equals 12) = 1/6 * 1/6 = 1/36
In my head, this is because (in the case of P(sum equals 6)), we have a 5/6 chance of rolling a 3 with the first die, and then we have a 5/6 chance of rolling a 3 with the second die.
However, when I apply this logic to P(sum equals 9), it doesn’t work, since my logic dictates that we have 5/6 chance of rolling 3 with the first die, and then 1/6 chance of rolling 6 with the second die.
But this doesn’t make sense, since P(sum equals 9) = 1 – P(sum equals 6) + P(sum equals 12)
So, I can only think that I’m thinking about this in a fundamentally incorrect way.
I can see that we can say P(sum equals 9) = 5/36 + 5/36, but I don’t understand why we would sum these? Doesn’t this mean that we are saying something like:
“the first die could be 3 and then the second die could be 6 OR the first die could be 6 and the second die could be 3”
Isn’t that wrong because it’s not relevant which die is rolled first? Why would the number of possible rolls double? Don’t we simply choose an arbitrary die and roll it? It seems like this is the inclusion-exclusion principle at work, but I don’t know how to put it in words that I can intuitively understand. Right now, it feels contrived, like I’m just guessing around and blindly following a formula.
✓ Extra quality
ExtraProxies brings the best proxy quality for you with our private and reliable proxies
✓ Extra anonymity
Top level of anonymity and 100% safe proxies – this is what you get with every proxy package
✓ Extra speed
1,ooo mb/s proxy servers speed – we are way better than others – just enjoy our proxies!
USA proxy location
We offer premium quality USA private proxies – the most essential proxies you can ever want from USA
Our proxies have TOP level of anonymity + Elite quality, so you are always safe and secure with your proxies
Use your proxies as much as you want – we have no limits for data transfer and bandwidth, unlimited usage!
Superb fast proxy servers with 1,000 mb/s speed – sit back and enjoy your lightning fast private proxies!
99,9% servers uptime
Alive and working proxies all the time – we are taking care of our servers so you can use them without any problems
No usage restrictions
You have freedom to use your proxies with every software, browser or website you want without restrictions
Perfect for SEO
We are 100% friendly with all SEO tasks as well as internet marketing – feel the power with our proxies
Buy more proxies and get better price – we offer various proxy packages with great deals and discounts
We are working 24/7 to bring the best proxy experience for you – we are glad to help and assist you!