Question

Kimiko and Miko are playing a game in which each person rolls a number cube. If the sum of the numbers is a prime number, then Miko wins. Otherwise, Kimiko wins. Is this game fair? Select the response with the correct answer and an argument that correctly defends the response. Multiple choice question. A) no; The probability that Miko will win is 712 . Because 712 is greater than 512 , Miko has a greater chance of winning. B) no; The probability that Kimiko will win is 712 . Because 712 is greater than 512 , Kimiko has a greater chance of winning. C) no; The probability that Kimiko will win is 812 or 23 . Because 23 is greater than 13 , Kimiko has a greater chance of winning. D) yes; The probability that Kimiko will win is 612 or 12 . Since Kimiko's probability of winning is 12 Miko's probability of winning must also be 12 .

Answer 1

Answer: Choice B)

No; the probability that Kimiko will win is 7/12. Because 7/12 is greater than 5/12, Kimiko has a greater chance of winning.

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Step-by-step explanation:

The prime number sums possible are: {2, 3, 5, 7, 11}

Below is the list of ways to reach those prime sums. Focus on the items in bold. The non-bolded numbers to the left are there to keep count of things.

1. 1+1 = 2
2. 1+2 = 3
3. 1+4 = 5
4. 1+6 = 7
5. 2+1 = 3
6. 2+3 = 5
7. 2+5 = 7
8. 3+2 = 5
9. 3+4 = 7
10. 4+1 = 5
11. 4+3 = 7
12. 5+2 = 7
13. 5+6 = 11
14. 6+1 = 7
15. 6+5 = 11

There are 15 items in that list out of 6*6 = 36 dice rolls total.

15/36 = 5/12 is the probability of Miko winning

1 - (5/12) = 7/12 is the probability of Kimiko winning.

Those two fractions (5/12 and 7/12) aren't the same, which means the game isn't fair.

Kimiko has a better chance of winning since 7/12 is larger than 5/12.

This is why choice B is the final answer.