Which of the following experiments are Bernoulli trials?
a. A die is tossed 4 times and we record the number obtained for each trial.
b. A die is tossed 4 times and we record whether or not the number obtained is odd for each trial.
c. A box contains 4 red and 6 blue balls. A ball is picked up from the box 3 times with replacement.
d. A box contains 4 red and 6 blue balls. A ball is picked up from the box 3 times without replacement.
My Work: I know the following
Bernoulli trials (p: parameter) have the following properties:
a. Each trial yields one of two outcomes: success (S) or failure (F).
b. P(S) = p and P(F) = 1-p
c. Each trial must be independent
So using the above I said
A) Not Bernoulli Trials as although the trials are independent, there's no success or failure defined here. What number do we identify as a success? It's not given so we can't apply Bernoulli Trials here.
B) Yes, this is Bernoulli Trials as there's a definitive success (Getting a odd number) and failure (getting a even number) and the trials are independent as well!
C) No...? There's no success condition or failure condition defined here (What's a success? what's a failure?) so not Bernoulli Trials. Although they are independent trials.
D) No, same reason as C and add on the fact that the trials aren't independent as there's no replacement.
Is my reasoning/logic correct? Especially with C and D? I feel like I may be overthinking it. Any help with better identifying Bernoulli Trials in experiments would be greatly appreciated!