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A dice dive involves rolling two dice. A player who rolls a 3,4, 10,11 or 12 wins 5 points. A player who rolls a 5,6,7,8 or o loses 5 points if the expected value of playing this game is to lose 5/3 a player will (win or lose) (5 or 10) points by rolling a 2

answer:

The game will lose by 1.94 points .

Explanation:

A player who rolls a 3, 4, 10, 11, or 12 wins 5 points and player who rolls a 5, 6, 7, 8, or 9 loses 5 points.

As two dice are rolled hence the total chances are ( 6 x 6) = 36.

The chances of 3 in rolling are (1,2), (2,1)

So the probability of rolling 3 is 2/36

The chance of 4 in rolling are (1,3),(3,1), (2,2)

So the probability of rolling 4 is  3/36

The chance of 10 in rolling are (5,5),(4,6), (6,4)

So the probability of rolling 10 is 3/36

The chance of 11 in rolling are (5,6),(6,5)

So the probability of rolling 11 is 2/36

The chance of 12 in rolling are (6,6)

So the probability of rolling 12 is   1/36

So the total probability of winning is ( 2/36) + ( 3/36) + ( 3/36) + ( 2/36) + ( 1/36) = 11/36

Hence the probability of losing is ( 1 - 11/36) = 25/36

So the expected value of the game

= (11/36) x 5 + (25/36) x (-5) = (55/36) - (125/36) = (- 70/36) = - 1.94

Therefore, the game will lose by 1.94 points

hope it helps

 ~ Maddy

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hope this : )