MHB How Do Ace Distributions Affect Probabilities in a Bridge Game?

WMDhamnekar
MHB
Messages
376
Reaction score
28
Bridge : For k= 1,2,3 ,4 let $N_k$ be the event that North has at least k aces. Let $S_k, E_k, W_k$ be be the analogous events for South, East, West. Discuss the number x of aces in West's possession in the events
a)$W_1', $
b) $N_2S_2,$

c) $N_1'S_1'E_1'$
d) $W_2- W_3$
e)$N_1S_1E_1W_1$

f) $N_3 W_1$
g)$(N_2 \cup S_2)E_2$

How to answer these questions? Truly speaking, I didn't follow these events. Would any member of math help board answer these questions along with explanation of these events?
 
Last edited:
Mathematics news on Phys.org
It helps to know the symbolism. In symbolic logic the prime, ', indicates that the statement is NOT true. Since we are told that [math]W_1[/math] means "West has at least one ace", [math]W_1'[/math] means "West does NOT have at least one ace". I.e. West does not have any aces.

Symilarly, two symbols written together indicate that they are both true. [math]N_2S_2[/math] means that "North has two at least aces and South has at least two aces".

The union sign, [math]\cup[/math], indicates "either or". [math](N_2\cup S_2)E_2[/math] means "Either North has at least two aces or South has at least two aces, and East has at least two aces.

Finally A- B means that statement A is true but statement B is false. [math]W_2- W_3[/math] means "West has at least two aces but West does not have at least three aces". I.e., West has exactly three aces.

Now you try the others.
 
County Boy said:
Finally A- B means that statement A is true but statement B is false. [math]W_2- W_3[/math] means "West has at least two aces but West does not have at least three aces". I.e., West has exactly three aces.

The last sentence should have been "West has exactly TWO aces".
 
County Boy said:
The last sentence should have been "West has exactly TWO aces".
The number x of aces in West's possession in the event $(a)W_1', (b)N_2S_2, (g)(N_2 \cup S_2)E_2$ is = 0.

The number of aces in West's possession in the event $(e) N_1S_1E_1W_1, (f)N_3W_1$ is = 1.

The number of aces in West's possession in the event $(d)W_2- W_3$ is = 2.

The number of aces in West's possession in the event $(c) N_1' S_1'E_1'$ is = 4.
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

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...
View full post »

Thread 'Fermat's Last Theorem'

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...
View full post »

Thread 'Useless continued fraction for 1'

I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
View full post »

Hot Threads

Recent Insights

Back
Top