Warm-up problem:
Roll 2 fair 6-sided dice. How often will at least 1 of them be a "1"?
Intermediate problem:
Roll 3 fair 6-sided dice. How often will at least 2 of them be a "1"?
Since there are 216 possible ways to roll 3 dice, give your answer in terms of "x outcomes out of a possible 216".
Advanced problem to follow later.
Ganchrow and RickySteve, please wait 24 hours to post.
Warm-up problem:
Roll 2 fair 6-sided dice. How often will at least 1 of them be a "1"?
1-1,1-2,1-3,1-4,1-5,1-6,2-1,3-1,4-1,5-1,6-1
11/36 = 31%
Intermediate problem:
Roll 3 fair 6-sided dice. How often will at least 2 of them be a "1"?
Since there are 216 possible ways to roll 3 dice, give your answer in terms of "x outcomes out of a possible 216".
41/216 = 19%
Advanced problem to follow later.
Ganchrow and RickySteve, please wait 24 hours to post.
what is the advance problem?
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"But you can't have your dream without laying something on the line. The key is not to risk what you can't afford to lose. You might think you're different, but someday you gonna want more too. The quesiton is what are you willing to lay on the line."
钱 錢 argent Geld soldi お金 돈 dinheiro деньги dinero เงิน כסף, ממון raha λεφτά pengar danh từ money
Your answer on the intermediate problem is incorrect. Perhaps if you gave your analysis on it, other people could help.
Instead of counting individual incomes for the warm-up, you might consider using a different approach that works better as the complexity goes up.
16/216=5%
__________________
"But you can't have your dream without laying something on the line. The key is not to risk what you can't afford to lose. You might think you're different, but someday you gonna want more too. The quesiton is what are you willing to lay on the line."
钱 錢 argent Geld soldi お金 돈 dinheiro деньги dinero เงิน כסף, ממון raha λεφτά pengar danh từ money
i think you can still count it. the 11 earlier with 3rd as 1 then add 1-1-2, 1-1-3, 1-1-4, 1-1-5, 1-1-6
__________________
"But you can't have your dream without laying something on the line. The key is not to risk what you can't afford to lose. You might think you're different, but someday you gonna want more too. The quesiton is what are you willing to lay on the line."
钱 錢 argent Geld soldi お金 돈 dinheiro деньги dinero เงิน כסף, ממון raha λεφτά pengar danh từ money
Location: Forest Hills, NY, Home of the Blitzkrieg Bop
Posts: 4,587
square's spreadsheet is right on point.
This question is provides a straightforward application of Bayesian inference where the availability of additional evidence is used to refine the prior probability distribution. I briefly explained the concept in this post and provided a couple of examples and a spreadsheet.
All those interested should check the above post and peruse the spreadsheets. As always feel free to ask any questions.
I'll try to post another problem of Bayesian inference more obviously related to sports betting at a later date.