Question

In a game, the numbers from 1 to 20 are written on tickets and placed in a bag. A player draws out a number at random. He or she wins 3$ if its even, 6$ if it is a square number and 9$ if its both even and square.
A.) Calculate the probability when he/she wins 3$, 6$ and 9$
B.) How much should be charged to play the game so that it is a fair game

Answer 1

Number Written from tickets=1-20

Total Cards=20

$\boxed{\mathbf{Probability=\frac{Favourable\: Outcomes}{Total\: Outcomes}}}$

Now,

$3=If Number is Even

$6 =If number is a square Number

$9 =If Number is Both Square and Even.

--------------------------------------------

(A).Even Number Between 1-20

=2,,6,8,10,12,14,,18,20

Total Even Number(Except 4 and 16) =8
We DOESN'T take 4 or 16 because it is both even and Square.

Total Outcomes=20

$\boxed{\mathbf{Probability (Even)=\frac{8}{20}}}$

$\boxed{\mathbf{Probability (Even)=\frac{2}{5}}}$

Probability of Winning $3=$\boxed{\mathsf{\frac{2}{5}}}$

------------------------------------------------------------

Square Number Between 1-20

2²=4

3²=9

4²=16

Total Square Number=3

Total Outcomes=20

$\boxed{\mathbf{Probability (Sqr\:no.)=\frac{3}{20}}}$

Probability of Winning $6=$\boxed{\mathsf{\frac{3}{20}}}$

---------------------------------------------------------

Number That Are Even and Square Both.

2²=4

4²=16

Total Number=2

Total Outcomes=20

$\boxed{\mathbf{Probability (Even\:Sqr\:no.)=\frac{2}{20}}}$

$\boxed{\mathbf{Probability (Even\:Sqr\:no.)=\frac{1}{10}}}$

Probability of Winning $9=$\boxed{\mathsf{\frac{1}{10}}}$

---------------------------------------------

(B)