Question

Justify whether or not the following is a binomial.

Rolling a fair die 3 times and observing the number of times a 6 is thrown.

I know that the binomial rules are :
1. The number of trials in the experiment is fixed.
2. There are two outcomes of each trial: "success" and "failure".
3. The probability of success in each trial is the same.
4. The trials are independent of each other.

1. Fixed - are 3 trials.
2. There is a success if it lands on 6 and failure if it lands on any number that is not 6.
success/p =1/6 fail/q=5/6
3. 1/6+5/6=1
4. I don't know how to put together the words to explain this.

Answer 1

For 4, if they're independent, it would look something like this right?
E= { SFF, SFS, SSF, FFS, FSS, FSF, FFF}
1 s 2s 2s 1s 2s 1s 0s
With s standing for success and the numbers being the number of successes.

Answer 2

(1/6)(1/6)(1/6) = 1/216
Independent means that the outcome of the first trial does not impact the second trial.
In this case good. yes independent
BUT if you had 6 cards numbered 1 to 6
and you drew the first and had the number 3
the chance was 1/6 of getting three.
HOWEVER if you do NOT put that BACK, the chance of getting three will be zero on the next draw and the chance of getting the number 2 will be 1/FIVE. Second draw therefore DEPENDENT on first draw..