Respuesta :

wegnerkolmp2741o

Answer:

Fair game

Step-by-step explanation:

Let us find the sample space.  It is the sum of the two spins

1+1 1+2 1+3  1+4 1+5 1+6

2+1 2+2  2+3  2+4 2+5 2+6

3+1 3+2 3+3 3+4 3+5 3+6

4+1  4+2  4+3  4+4 4+5 4+6

5+1  5+2 5+3 5+4 5+5 5+6

6+1 6+2 6+3 6+4 6+5 6+6

Adding

2,3,4,5,6,7

3,4,5,6,7,8

4,5,6,7,8,9

5,6,7,8,9,10

6,7,8,9,10,11

7,8,9,10,11,12

P(2) = 1/36

p(3) = 2/36

p(4) = 3/36

p(5) = 4/36

p(6) = 5/36

p(7) = 6/36

p(8) = 5/36

p(9) = 4/36

p(10) = 3/36

p(11) = 2/36

p(12) = 1/36

Player A wins if the sum is even

P(2,4,6,8,10,12) = P(2)+P(4)+P(6)+P(8)+P(10) + P (12) because the events are independent

               = 1/36 + 3/36+5/36+5/36+3/36 +1/36= 18/36 = 1/2


Player B wins if the sum is odd

P(3,5,7,9,11) = P(3)+P(5)+P(7)+P(9)+p(11) because the events are independent

               = 2/36 + 4/36+6/36 +4/36+2/36= 18/36 = 1/2

The probabilities are the same, so this is a fair game

musiclover10045

There are 36 different outcomes:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)


18 are even and 18 are odd

So there is a 50% chance to win, making it a fair game.


Otras preguntas

Q&A Education