MHB Probabilities of certain events in a lucky wheel game

AI Thread Summary
The discussion centers on a wheel of fortune game with ten equal sectors, where candidates K1 and K2 spin the wheel to determine a winner based on the numbers spun. To ensure at least one draw with a probability of at least 0.95, a minimum of seven candidate pairs must participate. The probability of a draw in a single match is calculated as 0.38, leading to the conclusion that at least seven matches are needed to achieve the desired probability. Additionally, the probability that at most 143 out of 376 matches end in a draw raises questions about the application of the binomial theorem. The conversation highlights the mathematical approach to determining probabilities in this game scenario.
emmi2104
Messages
1
Reaction score
0
Given information:
A wheel of fortune with ten equal sectors is used for a candidate game. Five of these sectors are labelled only with the number 1, three only with the number 2 and two only with the number 3.

The game for a pair of candidates is as follows: The two candidates �K1 and K2, independently of each other, each spin the wheel of fortune once. The winner is the candidate who has "spun" the higher number. If the numbers are the same, the game ends in a draw.

  • f) The game described above is played with 𝑛 pairs of candidates. What is the minimum number of candidate pairs with which the game must be played so that with a probability of at least 0.95 at least one game ends in a draw?
and
  • h) With what probability 𝑝 do at most 143 of the 376 matches end in a draw?
 
Last edited:
Mathematics news on Phys.org
I see this is an old unanswered question. Perhaps it was a homework problem at one time. I would start by finding out the probability of (not a tie) in a single match.
 
That would be 1 - (0.5^2+0.3^2+0.2^2) = 0.62
Now what's the minimum value of n s.t. 0.62^n <= 0.05? Trial and error (or taking the log of .05 base 0.62 and rounding up) says 7

Does h require the binomial theorem?
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Back
Top