Question

Kimiko and Miko are playing a game in which each girl rolls a number cube. If the sum of the numbers is a prime number, then Miko wins. Otherwise Kimiko wins. Find the sample space. Then find the probability that MIko wins.

Answer 1

Are they standard dice?

Answer 2

i fink so.. i'm pretty sure... :D

Answer 3

OK, so the sample space is all the possible outcomes. What are the possible outcomes of rolling two dice?

Answer 4

12?

Answer 5

Not exactly. Can we get an 11?

Answer 6

no?

Answer 7

Sure we can. If one rolls a five, and the other a six.

Answer 8

o

Answer 9

What's the smallest number we can roll on two dice?

Answer 10

1=1=2....i fink?

Answer 11

1+1=2 is wut i meant

Answer 12

Yep. So the sample space is \[\left\{ 2,3,4,5,6,7,8,9,10,11,12\right\}\]

Answer 13

Do you see how I got that?

Answer 14

11 choices?

Answer 15

Yes. Now, which are the prime numbers (the ones that let Miko win)?

Answer 16

4 prime numbers: 3,5,7,and 11?

Answer 17

Yes, and two also.

Answer 18

so da probability is 11/12?

Answer 19

Not quite. There is only one way (1,1) to roll a two. There are two ways to roll a three (1,2) and (2,1). How many ways are there to roll a five?

Answer 20

10?....

Answer 21

Not that many. Think about the dice; there aren't any zeros, so the least we could get on the first dice is a one. To add up to five, the other dice has to be a four (1,4). If the first die is a two, the other needs to be a three (2.3). The reverse orders will also work, (3,2) and (4,1) for a total of four ways. Get it?

Answer 22

yes..so the probability of MIko is...?

Answer 23

We're not there yet. There are two ways to get an eleven (5,6) and (6,5). That makes fifteen ways that Miko can win (one way to roll a two, two ways each to roll a three or an eleven, and four ways to roll a five, and six ways to roll a seven).

Answer 24

How many ways can the dice land?

Answer 25

6*6=36

Answer 26

YES!! So the probability of Miko winning is fifteen out of thirty-six. Simplified, it comes to five out of twelve, or 5/12.

Answer 27

ohhhhhhhhhhhhhhhh now i get it......ohhhh ic ur point now.. from b4.....oh dat's y... oh thank you sooo much, animalain..... :)

Answer 28

No problem. Did you have fun?

Answer 29

watcha mean?

Answer 30

Well, you got the answer; did you have fun?

Answer 31

yeppos :D u bet i did! *i call for a big 'high five dude!' !!!!!!!!!!!!!!!!!!!!

Answer 32

Back atcha!

Answer 33

mmmhmmmm, buddy... wut grade r u in?

Answer 34

Well, I might not be in school that has grades anymore.

Answer 35

ur in college????

Answer 36

I teach college math.

Answer 37

oh... ur such a genius!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! yay!!!!!!!!!!!! (i'm in middle skool :D)

Answer 38

Stay after it, and you can get good at math. That's the most important thing to being a good math student.

Answer 39

thx!

Answer 40

well, good nite to u....my friend...hehheh

Answer 41

but then i'm confused...isn't 2 (1 and 1) 2 isn't an even number... that means that Kimiko wins...but I thought we're trying to find,like, wut Miko's ODD probability is...and another question: isn't 9 an odd number? and 9 has 4 different ways right? and so overall,it should be 17 right? cuz well, if u add them all up(excluding the 2, bcuz then the 2 is an even number, then it should be sumthing like 17, rite?
So i basically think that the probability for Miko is...uh...17/36? I'm not sure if I'm right or not, becuz then, i only solved it according to ur explanations...so yeah...

Answer 42

The difference between prime and composite numbers isn't really about even and odd. Prime numbers are the ones that can't be divided evenly by anything but themselves and one. Two qualifies for this specification. On the other hand, as you noted, no other even number can be prime, since they can be divided by two. Odd numbers are not necessarily prime. Consider nine, for example. Nine can be factored to three times three, so it is composite, not prime.

Answer 43

-__- yeah, i know now...my tutor read it wrong...he said it was even and odd instead of prime... >:/ grrrr
but thank you VERY MUCH, anyways... ur of great help...
gtg eat dinner now.. c ya!