What is the average number of rolls of a die to get a 6?

Ok, let’s translate this into a simple question about rolling a die: How many times would you expect to roll a die to see a 6? The probability of getting a six in a single throw is 1/6. Therefore, on average, you’ll have about six throws for every appearance of a 6.

How often on average do you have to roll a die to see all six sides come up at least once?

about 15 times
(The numbers represent the order of the observed sides, not the values on the dice.) Adding all the expected number of rolls for each definition of success we get 14.7. So we expect to roll a die about 15 times on average before we observe all sides at least once.

When rolling a die 100 times what is the probability of rolling a 6 exactly 20 times?

Assuming that each roll is independent, you have a 1/6 chance of rolling a 6. You want to find the probability of it rolling a 6 twenty times out of 100, so we have (1/6)^20. Here the order doesn’t matter so multiply this by (100/20). For eighty times, you will have (5/6)^80 chance in rolling a die that is not a 6.

What are the odds of rolling three sixes?

If any of the dice are a 6 we payout based on the following. This seemed simple at first as the odds of rolling 1 six are 1/2, 2 sixes would be 1/14 and 3 sixes would be 1/216 so they would be our odds.

What is the average number of sixes in 100 rolls?

the probability of rolling a 6 on a fair die is 1/6, so that we expect 100 × 1/6 = 16.7 ≈ 17 6’s to be rolled.

How many times do you have to roll a dice to get every number?

From the numerical results, we can see that if we want to have at least 95\% probability of seeing all 6 faces, we need to roll at least 27 times.

How do you find the probability of exactly 3?

The number of outcomes with exactly 3 heads is given by (63) because we essentially want to know how many different ways we can take exactly 3 things from a total of 6 things. The value of this is 20. So the answer is 20/64=5/16.