# If you roll a fair die what is the theoretical probability of getting a 5?

Since there are 6 numbers on a die (1-6), then the probability of rolling a 5 would be 1 out of 6.

### How did theoretical probability get its name?

The theoretical probability of an event is the probability that is calculated on theoretical considerations. This normally entails modelling the experiment and then employing the laws of science to determine the event space and the probabilities of the outcomes. For example, suppose you wish to determine the theoretical probability of getting the number 5 when you roll a normal die. There are 6 possible outcomes. If the die is fair then each of these outcomes…

### What is the difference between theoretical probability and experimental probability?

The difference between experimental probability and theoretical probability is that experimental probability is the probability determined in practice. Theoretical probability is the probability that should happen. For example, the theoretical probability of getting any single number on a number cube is one sixth. But maybe you roll it twice and get a four both times. That would be an example of experimental probability.

### Experimental probability of rolling the sum of 2?

That means that you should roll a die many times, count how often you get the number "2", then divide this by the total number of rolls. If the die is "fair" (no extra weight on one side), you would expect this experimental probability to be somewhere close to the theoretical probability of 1/6, at least, if you roll often enough.

### How do you get if you roll a die 100 times how many times would you expect to get 1?

If you roll a die 100 times, you would expect to get a 1 about 17 times, because the probability of getting a 1 is 1 in 6, or 0.1667. However, that is theoretical probability; experimental probability - the actual results of doing this 100 times - might not be 17, but if you did this a large number of times, the experimental results would indeed begin to approach the theoretical results.

### What is the probability that you will roll a number less than 3 and flip heads if you roll a six sided die and toss a coin?

I am assuming that this die is fair die and the coin is not biased. The probability of getting a number less than 3 is the probability of rolling a 1 or a 2 i.e. 1/6 + 1/6 = 2/6 which simplifies to 1/3. The probability of getting a head when you flip a fair coin is 1/2. Both are independent events, so the probability of getting a number less than 3 and getting a…

### What is the difference between experimental probability and theoretical probability?

In experimental probability the probabilities of the outcomes are calculated as the proportion of "successful" outcomes in repeated trials. In theoretical probability these are calculated on the basis of laws of science being applied to a model of the experiment. For example, to find the probability of rolling a six on a standard die, you could roll the die many times (N) and count the number times that it comes up 6 (n). The experimental…

### What is the probability that you don't roll a sum of 3 when you roll two fair dice?

I think of it this way. Take it as two unique 6-sided dice, then you have 36 possible outcomes (6 times 6). Two of these outcomes will add to equal 3 (2 & 1, and 1 & 2), so there are 34 [36-2] outcomes which don't sum to 3. The probability is 34/36 or about 94.44 percent chance. If you're asking what the probability you don't roll AT LEAST three is, the only roll on…

### What is the probability that you roll a six and one and three?

If the order of the numbers matters, then: The probability of a 6 on the first roll is 1/6. The probability of a 1 on the second roll is 1/6. The probability of a 3 on the third roll is 1/6. The probability of all three is (1/6 x 1/6 x 1/6) = 1/216 = 0.00463 = 0.463 % (rounded) If you're not concerned about the order of the rolls, only the probability of getting…

### If you roll two die what is the probability that one die will roll a one and the second die will roll a two?

Assuming you are talking about fair, six-sided dice, then the probability of rolling a 1 on the first roll in 1/6, and the probability of rolling a 2 on the second roll is 1/6. Putting these together, the probability of rolling 1 on the first die and 2 on the second die is 1/36. If you do not care about the order, then you could roll 1,2 or 2,1; in this case the probability would…

### If you roll a fair die four times what is the probability of rolling a four on only the second throw?

The probability of rolling a 4 when you throw once a fair die is: P(4) = 1/6. The probability of not rolling a 4 when you throw once a fair die is: P(NO 4) = 5/6. If you roll a fair die four times, the probability of rolling a four on only the second throw is: P(NO 4, 4, NO 4, NO 4) = (5/6)(1/6)(5/6)(5/6) = 0.096450617... ≈ 9.6%