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## Statistics and probability

### Course: Statistics and probability>Unit 7

Lesson 5: Randomness, probability, and simulation

# Random numbers for experimental probability

AP.STATS:
UNC‑2 (EU)
,
UNC‑2.A (LO)
,
UNC‑2.A.4 (EK)
,
UNC‑2.A.5 (EK)
,
UNC‑2.A.6 (EK)
CCSS.Math:
Using a list of random number to calculate an experimental probability.

## Want to join the conversation?

• How would you do a mathematical calculation of the probability of winning this game?
• Just bit of logic, Maximum roll is 18 minimum roll is 3. This means we have total of 16 outcomes. Rolling below 10 has 7 values (3,4,5,6,7,8,9) and rolling 10 or more has 9 values. (10,11,12,13,14,15,16,17,18).
So you will have 43.75% chance to roll below 10 and 56.25% chance to roll above 10.

Maths
7/16 = 0.4375
9/16 = 0.5625
• Why not run RANDOM numbers from 1 to 6?
• Well he doesn't really control the random number generator, I think he just rang up a website that did a string of numbers a lot.
• how can we calculate the theoretical probability in this and the previous examples?
• As for me, in this particular example it is easier (for those who want to decide whether to participate in the game) to come up with the concept of expected value from theoretical probability.
If the 6-sided die is fair, then every result from 1 to 6 has a 1/6 probability. If in this case we take an expected value ('mean value' / 'average' for probability) of every toss - then we have 3,5 (we find this by multiplying each value (1,2,3,4,5,6) by 1/6 probability and summing them up).
As we have 3 tosses in this game - we multiply 3,5 by 3 and have 10,5. What does this value of 10,5 tell us? It tells that on average we are likely to win this game (remember the necessity of getting 10 as the sum of 3 rolls to win).
Correct me if I am wrong, please.
• I am confused. Why would we calculate experimental probability here when we can theoretically calculate the probability of getting a sum of 10 or more as 62.5%. I thought we use experimental probability only when it is impossible to calculate theoretical probability like the number of points scored in a football game in the previous example.
• You always have both options. Maybe you know how to calculate the theoretical probability here, but there may be others who do not. In cases where it is very difficult or you just do not know how to do it, it is nice to have an alternative to be able to approximate the answer.
• Is the probability about 14.63 for over a million experiments? I made a program that calculates it and wonder if it is right.
(1 vote)
• The probability should be roughly 62.5%
• Is there a website that can do that. Instead of a 10 times, 100 times?
(1 vote)
• Can anyone solve it theoretically
(1 vote)
• My question is similar to Zubair's in that I would like to know how to calculate the theoretical probability of something I have done experimentally. I have a dataset of 1296 unique codes which can be numbered 1 through 1296. I want to know if a number is picked each time at random, but returned to the dataset, on average, how many times it will be before you pick a number that you have already picked. Experimentally (programming) it averages out at 45.875 times before a duplicate is picked but I want to verify it with a calculation.
(1 vote)
• It's quite tricky. The probability of not having a match after the nth attempt is 1296!/((1296-n+1)! * 1296^(n-1)). You're not going to have an easy time from this point on.
(1 vote)
• those are not random your last tutorial used the same numbers