My friend and I have been debating back and forth on the answer to this question. I say that it is 1/6, while she says that it is 1/60. So, the question is...
If you are to roll a fair, six sided die ten times, what is the probability that you will roll a one for each roll?
I tried to make a diagram, which is how I got my answer, and my friend multiplied the chance of rolling a one by itself ten times, which is how she got her answer. Who is right, me, her, neither of us?
Prob(a one) = 1/6
prob(a one) twice = (1/6)(1/6) = (1/6)^2
..
prob(a one) ten times = (1/6)^10
= 1/60466176
= appr .000000016
These are independent events, that is, the die has no memory of what happened before, so each roll is a new event
e.g. suppose we flip a coin 3 times.
What is the prob of Tails, three times in a row.
According to my argument it is (1/2)^3 = 1/8
list them:
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT
There are 8 , only one is 3 tails
so 1/8