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, the die with the biggest value wins and if we get equal values the Black one wins. Which one of the dice has the biggest probability to win on throwing them both at the same time?
My solution:
P(red die for not rolling six) = 1 - 1/3 = 2/3Since 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 i am not really sure about this.
Please help!
My solution:
P(red die for not rolling six) = 1 - 1/3 = 2/3Since 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 i am not really sure about this.
Please help!
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