Probability puzzle is available on google app store:
it comprises of 3 levels of difficulty:
Outrageous:
- Foxes multiplied by hounds divided by the total 5*7/12
Answer: 5*7/12 - It’s every permutation of two different digits I used E (east) and N (north), were there is 7 E and 4 N which equals 330
Answer: 330 - 1 minus all possible ways for the mouse to reach the trap multiplied by the ways to get from the trap to the cheese divided by 330 equals 1-621/330
Answer: 1-621/330 - Ok, so this one is a little tricky, first you can see that train B will be there in 3 minutes no matter what happens with train A. So if Train A does not arrive in 3 minutes or less then the average is 1.5 minute wait time which occurs 2/5 of the time. Now if Train A does make it in the firs 3 minutes then the average wait time between both trains is 1 minute which occurs 3/5 of the time. So the equation is (1.52/5)+(13/5)
Answer: (1.52/5)+(13/5) - There us 13 positions possible to make a couple, 13 seats, with 5 men, and 8 women in a round table.
Answer: 13(8/135/12+5/138/12) - Same as the top question except we lose possible chance to make a couple.
Answer: 12(8/135/12+5/138/12) - There is no correlation, however since it’s those in college the high math or English skills allow you in without the other so it becomes -0.5
Answer: -0.5 - The hat party, If there was 10 people at the party then there would be a 1/10 chance of each getting the same hat, so the chance of no one getting the same hat is 0.9^10. So the chance of at least 1 hat going to the same person is 1-0.9^10. This is almost our answer we just need to be more significant so 1-0.99999^100000
Answer: 1-0.99999^100000 - This is almost exactly the same question as getting serious question 18. Not only can it be done the exact same way but it also uses the same number so it is the same answer (1/3)(1/3)
Answer: (1/3)(1/3) - Answer: 92378
- This is another logic question, the answer is 1
Answer: 1 - The round table coin game, so I would like to talk about how I approached this, first I tried 1/6, the amount of people still playing, and that didn’t work, then I read the hint and that made me think that it’s a 50-50 chance for every person sitting next to an eliminated player, I really thought this made sense, so I tried 0.5^5 but that was wrong too; so I looked it up and it said the chances are 1/(n-1), so I tried 1/6 again and 1/5 but both were wrong. I then tried 1/9 (which to me insinuate that there is no eliminated players) and that turned out to be right but I don’t understand why, so answer is 1/9 and the source is here https://mathgems.wordpress.com/2010/11/12/random_chair/
If someone knows why please post because I don’t understand it.
Answer: 1/9 - Answer: 10
- Answer: 18
- Answer: 30-18 = 12
- Answer: 0.5*(1 + e^(-2))
- Answer: 1/42
- Answer: 40/100
don’t forget to check the earlier levels: Getting serious
Thanks for Ralph for all these answers.
Kalamawi 
1. Foxes multiplied by hounds divided by the total 5*7/12
2. It’s every permutation of two different digits I used E (east) and N (north), were there is 7 E and 4 N which equals 330
3. 1 minus all possible ways for the mouse to reach the trap multiplied by the ways to get from the trap to the cheese divided by 330 equals 1-6*21/330
4. Ok so this one is a little tricky, first you can see that train B will be there in 3 minutes no matter what happens with train A. So if Train A does not arrive in 3 minutes or less then the average is 1.5 minute wait time which occurs 2/5 of the time. Now if Train A does make it in the firs 3 minutes then the average wait time between both trains is 1 minute which occurs 3/5 of the time. So the equation is (1.5*2/5)+(1*3/5)
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5. There us 13 positions possible to make a couple, 13 seats, with 5 men, and 8 women in a round table, so 13*(8/13*5/12+5/13*8/12)
6. Same as the top question except we lose possible chance to make a couple so 12*(8/13*5/12+5/13*8/12)
7. There is no correlation, however since it’s those in college the high math or English skills allow you in without the other so it becomes -0.5
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9. This is almost exactly the same question as getting serious question 18. Not only can it be done the exact same way but it also uses the same number so it is the same answer (1/3)*(1/3)
11. This is another logic question, the answer is 1
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Puzzle 8. The hat party
If there was 10 people at the party then there would be a 1/10 chance of each getting the same hat, so the chance of no one getting the same hat is 0.9^10. So the chance of at least 1 hat going to the same person is 1-0.9^10. This is almost our answer we just need to be more significant so 1-0.99999^100000
Btw your link from getting serious to outrageous doesn’t work, the only way for me to get here is the link in the comments.
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12. The round table coin game, so I would like to talk about how I approached this, first I tried 1/6, the amount of people still playing, and that didn’t work, then I read the hint and that made me think that it’s a 50-50 chance for every person sitting next to an eliminated player, I really thought this made sense, so I tried 0.5^5 but that was wrong too; so I looked it up and it said the chances are 1/(n-1), so I tried 1/6 again and 1/5 but both were wrong. I then tried 1/9 (which to me insinuate that there is no eliminated players) and that turned out to be right but I don’t understand why, so answer is 1/9 and the source is here https://mathgems.wordpress.com/2010/11/12/random_chair/
If someone knows why please post because I don’t understand it.
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Sorry I haven’t posted in a bit, it took me a while to solve some of these and I forgot to post, I don’t remember how I got most of these so I’m not going to post the work
10. 92378
13. 10
14. 18
15. 30-18 = 12
16. 0.5*(1 + e^(-2))
17. 1/42
18. 40/100
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Have you read this post yet?
https://kalamdeveloper.wordpress.com/2018/07/21/random-thought-i-need-your-opinion
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