00:01
For this exercise, we have six dice are rolled, and we are asked to find the probability of getting exactly one ace, at least one ace, or exactly two aces.
00:14
Now, i assume here what is meant by ace is one.
00:18
So we have an experiment where the number of rows is six.
00:23
The probability of getting a one, that's called that p, is one over six because there is one on the die and there are six faces on the die.
00:31
Let's define a random variable x as the number of aces in six rolls.
00:47
So here each of the six dyes can be considered a bernoulli trial, where there's two possible outcomes.
00:53
Either it's an ace or it is not.
00:57
And each trial can be considered independent because the outcome for one die has no bearing on the outcomes for the other five dice.
01:04
Dice.
01:06
And so the number of successes or the number of aces in a given number of independent bernoulli trials is a binomial random variable.
01:16
So x is a binomial random variable.
01:27
The probability mass function for the binomial random variable is given by this formula...