Advanced Math/Maths


Hi sir pls help thanks in advance
My friend and I are in a debate based on a problem containing probability.

what is the probability of guessing the correct out come of 14 football matches (28 unique teams) with 3 possible outcomes in each match (Win draw and loss)

my logic says it is 1/3^(14),
but he debates it is [(1/3)*(2/3)*(2/3)]^14

can you please tell me the solution.

Assuming they all have equal chance (which they don't, but we'll ignore that for now),
each has a probability of 1/3.  That is, 1/3 the time is a win, 1/3 the time is a loss,
and 1/3 the time is a draw.

Since there are 14 games, and each game has a 1/3 chance of being correct on the guess,
it is (1/3)^14.

The number 2/3 is the chance of guessing a game incorrectly.
That means the chance of guessing each game incorrectly is (2/3)^14.

If that's good, that's enough for you.
To give an even better understanding, though, read on...

The chance of guessing n games correctly (where n is an integer between 0 and 14) is given by
[(n choose 14)][(1/3)^n][(2/3)^(14-n)].

To say what "a choose b" means, it is a!/(b!(a-b)!) where '!' is used for factorial.
By this, 1! = 1;
2! = 2*1! = 2;
3! = 3*2*1 = 3*2! = 3*2 = 6;
4! = 4*3*2*1 = 4*3! = 4*6 = 24;
5! = 5*4*3*2*1 = 5*4! = 5*24 = 120;
6! = 6*5! = 6*120 = 720;
7! = 7*6! = 7*720 = 5,040;
8! = 8*7! = 40,320;
9! = 9*8! = 362,880;
10! = 10*9! = 3,628,800;
11! = 11*10! = 39,916,800;
12! = 12*11! = 479,001,600;
13! = 6,227,020,800; and
14! = 87,178,291,200.

Now if, for example, you only wanted 4 guesses to be correct, it would be the following:

Putting in 4 for x gives (14 choose 4)[(1/3)^4][(2/3)^10].

Now 14 choose 4 would be 87,178,291,200/(24*3,628,800).

Rather than doing it this way, a better way would be to note that 14!/10! = 14*13*12*11,

That makes the chance of guessing 4 correctly be (24,024/24)[(1/3)^4][(2/3)^10].

Note that 24,024/24 = 1,001, (1/3)^4 = 1/81 and (2/3)^10 = 1,024/59,049.
This means that the answer is given by 1,001(1/81)(1,024/59,049).
That comes down to you 1,025,024/4,782,969 = 0.214307055.  

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Scott A Wilson


I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can also say that I broke 5 minutes for a mile, which is over 12 mph, but is that relevant?


Experience in the area; I have tutored people in the above areas of mathematics for over two years in I have tutored people here and there in mathematics since before I received a BS degree back in 1984. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

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I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

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My clients have been students at OSU, people who live nearby, friends with math questions, and several people every day on the PC. I would guess that you are probably going to be one more.

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