2. Carnival Toss ? no lines touching: A game consists of tossing disks onto a ta

Question

2. Carnival Toss ? no lines touching: A game consists of tossing disks onto a table marked in squares of side a. If the disk does not touch any line or edge, the player wins. It is assumed that the player can at least hit the table. If r is the radius of the disk, what should the ratio r/a be if the game operator wants a player to have a chance of less than p of winning. 3. Carnival Toss ? at most one line touching: in the disk tossing game above, if the player is allowed to win whenever the disk touches zero or one line, but not two lines, what is the probability of winning? What is the percentage increase in the probability of winning by allowing the disk to touch at most one line compared to no lines?

Explanation / Answer

let r be the radius of the disks ,
so ,
the area (say A) which the centre of disk is allowable to go is
will be area af a square of side ( a-r).
A = (a-r)^2
so ,

P(f not touching the side of square ) = A/(area of table(which is square)

P = (a-r)^2/a^2 ,
given ,

(a-r)^2/a^2 < p ,
so ,

(a-r )/ a < p
therfore,

1- r/a< p ,

and,

r/a > (1+p).

2.
atmost touchiing one line means ,it shoul touch 0 or 1 line .
So , now the disk cannt go in corners ,
so ,
maximum allowable area for centre will be ,
A = a^2 - 4*(2r)^2, = a^2 - 16r^2
so ,
P` = (a^2-16r^2) /a^2 ,

increase,

delta P = P'-P = (a^2-16r^2) /a^2 - (a-r)^2/a^2

delta P = ( a^2-16 r^2 -a^2 -r^2 + 2ar )/a^2

delta P = ( 2ar- 16r^2)/a^2

% increase = [( 2ar- 16r^2)/a^2 ]*100/ (a-r)^2/a^2

% increase = ( 2ar- 16r^2)*100/ (a-r)^2

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.