Define an appropriate random variable X and give its parameters.?

Question

The question relates to the statistics problem:

Now suppose that you play 10 consecutive games of craps. We are interested in studying how many times you win on the first roll in these 10 games.

The chance of winning in craps is .222 by rolling a 7 or 11 with two die.

Yes, this is stat homework for all who are wondering.

Please help.

Answer 1

Here you have the following properties:

There is a set number of trials in advance. (10 consecutice games of craps)
The probability of success is the same from trial to trial. (success is getting a 7 or 11 and the probability of sucess is 0.222)
The trials are independent. (successive die rolls are independent)

Thus, you have a binomial distribution. The parameters are:

The number of trials (n) is 10.
The probability of success (p) is 0.222.

Answer 2

The chances of rolling a 7 or 11 on the first roll of the dice is
1 in 9. Hence the chance of rolling a 7 or 11 on the first roll in 10 games should be >= 1.

Answer 3

The probability of .222 is too high for a Poisson distribution to approximate the exact distribution you need, the binomial. p=.222 and q=.778