Probability - rolling a fair die 10 times, what is the probability you would match a separate set of 10 numbers?

Question

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

Thanks!

Answer 1

Yes, it is correct. To work out $P(9 or 10)$, you work out $P(9)$+$P(10)$. $P(9)$ is the probability that 9 are correct and 1is not. So, $P(9)$ = $10 \choose 9$* $ \frac{1}{6}^9$*$\frac{5}{6}^1$. Similarly, you get the answer for 10 correct as you did.