I am playing a dice game with my friend Kyle. Each of us roles a standard six-side die obtaining a number at random from 1 to 6. What is the probability that my number is greater than Kyle’s number?
draw a 6 by 6 grid of boxes
There are 36 boxes
but the ones along the diagonal are equal for each so only count those above the diagonal
There are six of those along the diagonal, 1,1 and 2,2 and 3,3 etc
so
I see 15 boxes above the diagonal
so I think 15/36
Emma,10 In regards to Oscar, I think that most torldeds are picky at some point. I think all parents of torldeds would say that some days they eat quite a bit, and then the next day they eat nothing. Feeding a toddler can be frustrating. It sounds like you are trying really hard and doing a great job Emma. Even if he is stuck on certain things, just keep adding healthy things to his plate that he doesn't like and don't stress about if he eats it or not, and someday he will! Even if Betty is picky about textures, I bet that if you experiment enough, you will find really healthy things that she will eat, even if she doesn't like a lot of foods still. OH, and if she is weird about textures, you may try mixing her veggies into her smoothie with the fruits to h elp with getting used to the taste. Gabe definitely has a pickier personality, but I don't stress too much over it, because there are a lot of healthy foods he will eat. OKay, now I am rambling, but all you can do is your best in the situation, and you are great!Wendy,I've always been impressed with how you feed your kids! I love the idea of the veggie/cheese/bread/nut tray. That would be such an easy thing to do for summer. Throw on some almonds, blueberries, hummus, veggies, and bread. I am so doing that, and I bet if the kids help put it together, they would love that too!!
To find the probability that your number is greater than Kyle’s number in this dice game, we need to compare all the possible outcomes for your roll against all the possible outcomes for Kyle’s roll.
Both of you can get any number from 1 to 6, and there are 6 possible outcomes for each of you. Therefore, there are a total of 6 * 6 = 36 possible outcomes for rolling two dice.
To determine the number of outcomes where your roll is greater than Kyle’s roll, we can create a table to represent all the possible outcomes:
Kyle's Number | Your Number
--------------|-------------
1 | 2, 3, 4, 5, 6
2 | 3, 4, 5, 6
3 | 4, 5, 6
4 | 5, 6
5 | 6
6 |
From the table, we can count that there are 15 possible outcomes where your number is greater than Kyle’s number.
Therefore, the probability that your number is greater than Kyle’s number is 15/36, which can be simplified to 5/12.
To find this probability, first, divide the number of favorable outcomes (15) by the total number of possible outcomes (36):
15 / 36 ≈ 0.4167
Then, convert the decimal to a fraction:
0.4167 = 5/12
So, the probability that your number is greater than Kyle’s number in this dice game is 5/12.