csc2iffy said:Homework Statement
If someone could just check my work, thanks!
If five dice are rolled once each, what is the probability of rolling exactly 4 identical numbers?Homework Equations
The Attempt at a Solution
This is what I have:
(1)(1/6)(1/6)(1/6)(5/6)=5/1296
csc2iffy said:Ok, so would it be this instead?
(6)(1/6)3(5/6)
csc2iffy said:i'm not sure, this is one of my study guide questions and this is why I'm asking...
csc2iffy said:I took a break from this problem but here is my newest attempt:
choose(5,4) = 5
so is it... 5(1/6)3(5/6)?
csc2iffy said:Homework Statement
If someone could just check my work, thanks!
If five dice are rolled once each, what is the probability of rolling exactly 4 identical numbers?
Homework Equations
The Attempt at a Solution
This is what I have:
(1)(1/6)(1/6)(1/6)(5/6)=5/1296
The probability of rolling four identical numbers with four six-sided dice is 1 in 1296, or approximately 0.077%. This is because there are 1296 possible outcomes when rolling four dice (6^4), and only 1 of those outcomes results in four identical numbers.
The probability of rolling four identical numbers with four eight-sided dice is 1 in 4096, or approximately 0.024%. This is because there are 4096 possible outcomes when rolling four dice (8^4), and only 1 of those outcomes results in four identical numbers.
Yes, it is possible to roll four identical numbers with four ten-sided dice. The probability of this occurring is 1 in 10,000, or approximately 0.01%. This is because there are 10,000 possible outcomes when rolling four dice (10^4), and only 1 of those outcomes results in four identical numbers.
The probability of rolling four identical numbers with four six-sided dice is 1 in 1296, while the probability of rolling four identical numbers with four ten-sided dice is 1 in 10,000. This means that it is approximately 7.7 times more likely to roll four identical numbers with four six-sided dice compared to four ten-sided dice.
Yes, the probability changes as the number of dice increases. The more dice you have, the lower the probability of rolling four identical numbers becomes. This is because the number of possible outcomes increases with each additional die, making it less likely for all of them to be the same number.