Math Expert Joined: 02 Sep 2009 Posts: 87961
What is the probability of rolling three six-sided dice, and getting a [#permalink]
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Question Stats: Hide Show timer StatisticsWhat is the probability of rolling three six-sided dice, and getting a different number on each die?A. 1/12B. 1/3C. 4/9D. 5/9E. 7/18 Kudos for a correct solution. _________________
Math Expert Joined: 02 Sep 2009 Posts: 87961
What is the probability of rolling three six-sided dice, and getting a [#permalink]
Bunuel wrote: What is the probability of rolling three six-sided dice, and getting a different number on each die?A. 1/12B. 1/3C. 4/9D. 5/9E. 7/18 Kudos for a correct solution. MAGOOSH OFFICIAL SOLUTION For the first die, we can roll any one of six numbers. For the second die, we can roll any number save for the number we rolled on the first die, giving us 5 possibilities. For the third die, we can roll four different numbers (we can’t roll the number we rolled on the first or second die.6 x 5 x 4 = 120 possibilities out of 216 total possibilities. (For total possibilities we get 6 x 6 x 6 = 216).120/216 = 5/9Answer: D. _________________
Re: What is the probability of rolling three six-sided dice, and getting a [#permalink] three dices were rolledtotal outcome 6x6x6different number should appear on eachfavorable outcome= 6c1*5c1*4c1probability= favorable/totalans=(6*5*4)/(6*6*6)= 5/9ans= D _________________
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Retired Moderator Joined: 30 Jul 2013 Status:On a mountain of skulls, in the castle of pain, I sit on a throne of blood. Posts: 264
Re: What is the probability of rolling three six-sided dice, and getting a [#permalink]
Bunuel wrote: What is the probability of rolling three six-sided dice, and getting a different number on each die?A. 1/12B. 1/3C. 4/9D. 5/9E. 7/18 Kudos for a correct solution. 6/6 * 5/6 * 4/6=5/9Answer: D
Manager Joined: 17 Mar 2015 Posts: 108
Re: What is the probability of rolling three six-sided dice, and getting a [#permalink] odds of rolling number on 1 dice is 1/6odds of rolling another number on 2nd dice is 5/6odds of rolling a number different from dice 1 and dice 2 on 3rd dice is 2/3there are 6 total numbers so the resulting probability is6*1/6*5/6*2/3 =10/18 = 5/9 D
Manager Joined: 25 Feb 2014 Posts: 190
Re: What is the probability of rolling three six-sided dice, and getting a [#permalink] 1 Possible combinations with three different numbers on each die when three dies are rolled = 6*5*42 Total no. of combinations of numbers with three dies = 6*6*6Divide 1 by 2 and we will get the probability = 6*5*4/6*6*6 = 5/9. Therefore ans is D.
Manager Joined: 01 Jan 2015 Posts: 50
Re: What is the probability of rolling three six-sided dice, and getting a [#permalink] Prob of rolling 1st die and getting any number(Lets say x) = 6/6 = 1Prob of rolling 2nd die and getting any number(Lets say y) but x = 5/6 Prob of rolling 2nd die and getting any number(Lets say z) but x and y = 4/6Total prob = 1 x 5/6 x 4/6 = 5/9 Ans D
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Re: What is the probability of rolling three six-sided dice, and getting a [#permalink]
We need to find What is the probability of rolling three six-sided dice, and getting a different number on each die?As we are rolling three six-sided dice => Number of cases = \(6^3\) = 216We need to get different number on each die=> First dice can get any of the 6 numbers=> Second dice can get any of the 5 numbers (Except the one which first dice got)=> Third dice can get any of the 4 numbers ((Except the two numbers which the first and the second dice got)=> Total number of ways = 6 * 5 * 4 => Probability of getting a different number on each die = \(\frac{6 * 5 * 4}{6^3}\) = \(\frac{5}{9}\) So, Answer will be D Hope it helps!Watch the following video to learn How to Solve Dice Rolling Probability Problems _________________
Re: What is the probability of rolling three six-sided dice, and getting a [#permalink] 09 Oct 2022, 09:03 |
What is the probability of rolling three dice and getting a different number on each die?
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