Calamitous Clod rolls a pair of rigged dice. The probability of rolling k on a die is directly proportional to k. What is the probability that the sum of Calamitous Clod's dice is equal to 7?

Thanks!

EpicWater Feb 4, 2020

#1**+2 **

Calamitous Clod rolls a pair of rigged dice. The probability of rolling k on a die is directly proportional to k.

What is the probability that the sum of Calamitous Clod's dice is equal to 7?

Mmmm. Am I supposed to assume that these are 6 sided dice?

Prob(rolling1) = k Where k is less than 1

Prob(rolling 2) = 2k

P(3) = 3k

..

P(6)=6k

k(1+2+3+4+5+6)=21k

21k=1 so

\(k=\frac{1}{21}\)

1 | 2 | 3 | 4 | 5 | 6 | |
---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 |

2 | 3 | 4 | 5 | 6 | 7 | 8 |

3 | 4 | 5 | 6 | 7 | 8 | 9 |

4 | 5 | 6 | 7 | 8 | 9 | 10 |

5 | 6 | 7 | 8 | 9 | 10 | 11 |

6 | 7 | 8 | 9 | 10 | 11 | 12 |

\(P(throwing 7) \\ = 2[P(1,6)+P(2,5)+P(3,4)]\\ =2[ k*6k + 2k*5k + 3k*4k]\\ =2k^2 (6+10+12)\\ =56k^2\\ =\frac{56}{441}\\ =\frac{8}{63}\)

You need to check what I have done.

It has been pointed out to me that k is the number on the die. I should have used a different letter for the proportionality constant.

If you change all my k's to a different letter, it would be a much better answer

Melody Feb 4, 2020