If necessary consult a list of formulas A fair die is rolled

(If necessary, consult a list of formulas.)

A fair die is rolled times. What is the probability of having no and no among the rolls? Round your answer to three decimal places. (If necessary, consult a list of formulas.)

Solution

the probability of getting any number is 1/6 and since the dice will roll 5 times, we get:

1/6*1/6*1/6*1/6*1/6= 1/7776

Now we are looking for two numbers (1 and 3) and the order does not matter. This means they are independent events.
Independent events: Two events are independent when the outcome of the first event does not influence the outcome of the second event.
When we determine the probability of two independent events we multiply the probability of the first event by the probability of the second event.

The possible outcome orders are:
1) 1 and 3
2) 3 and 1

Since the order does not matter, we have 2 possible outcomes. Resulting:

2*1/6*1/6*1/6*1/6*1/6= 1/3888= 0.000257.