Question

If I roll a fair, regular six-sided die four times, what is the probability that I will roll the number exactly three times

1. Latifah
The probability that I will roll the number exactly three times is 0.0038.
According to the statement
we have given that the a six-sided die is rolled a four times and we have to find the probability that I will roll the number exactly three times.
So, We know that the
Probability is the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.
And the probability of rolling any number on the die is 1/6.
And
when i want to get a exactly three number than the probability become:
So,
The probability that I will roll the number exactly three times = 1/6 *1/6 *1/6 *5/6
Then solve it
The probability that I will roll the number exactly three times = 1/216 * 5/6
here 5/6 is the probability of that numbers which are not come.
So,
The probability that I will roll the number exactly three times = 5/1296
The probability that I will roll the number exactly three times = 0.0038.
So, The probability that I will roll the number exactly three times is 0.0038.