Having some trouble with this problem...
Say someone is rolling a fair die 10 times, and using that roll as an attempt to guess what number (1-6) someone else has written down on a piece of paper for each roll. So, for each roll of the die, there is a separate number that we're trying to match. Each roll is independent. What is the probability that each roll will match the number written down? What is the probability that 9 or 10 of the rolls will match the number written down?
So, I know the probability for each roll is 1/6. E=1, S=6, P(E/S)=1/6. The prob of getting a wrong roll is 1-(1/6) = 5/6.
Now, how do I get the probability of matching 9 or 10 of the numbers? I'm thinking I need to use Bernoulli trials to figure out prob of 9 and 10, and sum them together.
Is this correct?
c(10,9) * (1/6)^9 * (5/6)^1 + c(10,10) * (1/6)^10 * (5/6)^0