probability

[native oracle]

hii can someone help me understand how to get the answers for this? i rrly need to understand cause its our finals tmrw

[forest vale]

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[unborn nebula]

31-40) Jason (Player 1) and John (Player 2) are playing a game called "Dice on me". The following are the rules.
i. Toss a pair of dice per round
ii. For each round, if the sum of the numbers is greater than 6, that would be a point for player 1. if the sum of the numbers is less than or equal to 6, that would be a point for player 2.
iii. After 10 rounds, the player who got the most points would say "Dice on me!" and wins the game.

Question: if you were to play the game, would you accept the result if you opponent wins? Do you think the game is fair? (Write your answer to these questions in the last row of the table given below)

Create a sample space for the experiment (3 points)

How many of the outcomes would generate a sum greater than 6? (1 point)

How many of the outcomes would generate a sum less than or equal to 6? (1 point)

Who would more likely win the game? (1 point)

Do you think the game is fair? Explain your answer based on your answers to the questions above. (2 points)

thats mostly for me and for anyone else who may help cos its hard to read

using the sample space you could sum the numbers on the dice and see how many outcomes would generate a sum "greater than" or "less than or equal" to 6, and use that as your answers to the second two questions

for the probabilities you use your prior answers (q2 and q3) and divide them by the total. so for "What is the probability of getting a sum greater than 6" you look at "how many of the outcomes would generate a sum greater than 6?" which you obtain from the sample space, and the answer to that is 21 therefore you do 21 over 36 (the total, 6^2, since you're multiplying the outcomes of one die by the other's)

Who would be more likely to win the game? Well since 7 is the highest probability roll with two dice you can just say that it's the person who has the outcome "greater than 6" (Jason), but if you didn't know about 7's with 2 dice, you could look at the probabilities of each outcome and use the higher one (What is the probability of getting a sum greater than 6 as compared to what is the probability of getting a sum less than or equal to 6?)

As for the last box, No, the game is not fair, because the probabilities of both players are not equal, so the game is biased towards one player winning. You need a reason as to WHY it isnt fair, simply putting yes or no makes it look like a guess so you have to back that up with a reason

if thats unclear feel free to ask

ofcourse that is all under the assumption that the dice are fair

[native oracle]

sorry but i didnt get the Q3 the how many outcomes would generate a sum greater than 6

[unborn nebula]

so you sum the numbers on the dice in the sample space, and then you add up the number of outcomes which are more than 6

so uh

one sec

You add up the number of yellow outcomes

since they all equal atleast 7

so greater than 6

[native oracle]

oh i get it thank you sm^^