ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sat, 04 Jul 2015 07:35:31 +0200Probability dice question, need to know if i am right?https://ask.sagemath.org/question/27257/probability-dice-question-need-to-know-if-i-am-right/Suppose that we have 2 dice, one Red and one Black. The Red die is defective, the probability to get 6 is 1/3. Now if we throw the 2 dice and get equal values the Black one wins, obviously if one is bigger that one wins. Which one of the dice has the biggest probability to win?
My solution:
P(red die for not rolling six) = 1 - 1/3 = 2/3
Since there are 5 other possible values we have P(red die for each value) = 2/3 * 1/5 = 2/15
Now for the Red Die to win we have 15 possibilities: (1,2) (1,3) (1,4) (1,5) (1,6*) (2,3) (2,4) (2,5) (2,6*) (3,4) (3,5) (3,6*) (4,5) (4,6*) (5,6*) => Of which 5 have 6 in it. While for the Black one 21 of which 1 have 6 in it.
P(red to win) = 10 * (1/6 * 2/15) + 5 * (1/6 * 1/3) = .5
P(black to win) = 20 * (1/6 * 2/15) + 1 * (1/6 * 1/3) = .5
Both have equal possibilities to win, however from some teacher notes it says that the Black one has the biggest probability to win and i don't know why.
Please help!Sat, 04 Jul 2015 02:36:44 +0200https://ask.sagemath.org/question/27257/probability-dice-question-need-to-know-if-i-am-right/Comment by rws for <p>Suppose that we have 2 dice, one Red and one Black. The Red die is defective, the probability to get 6 is 1/3. Now if we throw the 2 dice and get equal values the Black one wins, obviously if one is bigger that one wins. Which one of the dice has the biggest probability to win?</p>
<p>My solution:</p>
<p>P(red die for not rolling six) = 1 - 1/3 = 2/3</p>
<p>Since there are 5 other possible values we have P(red die for each value) = 2/3 * 1/5 = 2/15
Now for the Red Die to win we have 15 possibilities: (1,2) (1,3) (1,4) (1,5) (1,6<em>) (2,3) (2,4) (2,5) (2,6</em>) (3,4) (3,5) (3,6<em>) (4,5) (4,6</em>) (5,6*) => Of which 5 have 6 in it. While for the Black one 21 of which 1 have 6 in it.</p>
<p>P(red to win) = 10 * (1/6 * 2/15) + 5 * (1/6 * 1/3) = .5
P(black to win) = 20 * (1/6 * 2/15) + 1 * (1/6 * 1/3) = .5</p>
<p>Both have equal possibilities to win, however from some teacher notes it says that the Black one has the biggest probability to win and i don't know why. </p>
<p>Please help!</p>
https://ask.sagemath.org/question/27257/probability-dice-question-need-to-know-if-i-am-right/?comment=27258#post-id-27258Please ask on a site for math questions. This one is about using the Sage software system.Sat, 04 Jul 2015 07:35:31 +0200https://ask.sagemath.org/question/27257/probability-dice-question-need-to-know-if-i-am-right/?comment=27258#post-id-27258