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What is the probability of rolling three six-sided dice, and getting a

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Bunuel
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What is the probability of rolling three six-sided dice, and getting a [#permalink] What is the probability of rolling three six-sided dice, and getting a   14 Apr 2015, 05:14
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What is the probability of rolling three six-sided dice, and getting a different number on each die?

A. 1/12
B. 1/3
C. 4/9
D. 5/9
E. 7/18

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D
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Bunuel
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What is the probability of rolling three six-sided dice, and getting a [#permalink] What is the probability of rolling three six-sided dice, and getting a   20 Apr 2015, 06:26
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Bunuel wrote:
What is the probability of rolling three six-sided dice, and getting a different number on each die?

A. 1/12
B. 1/3
C. 4/9
D. 5/9
E. 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 = 5/9

Answer: D.
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Re: What is the probability of rolling three six-sided dice, and getting a [#permalink] What is the probability of rolling three six-sided dice, and getting a   14 Apr 2015, 05:29
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three dices were rolled
total outcome 6x6x6
different number should appear on each
favorable outcome= 6c1*5c1*4c1

probability= favorable/total

ans=(6*5*4)/(6*6*6)= 5/9


ans= D
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Re: What is the probability of rolling three six-sided dice, and getting a [#permalink] What is the probability of rolling three six-sided dice, and getting a   14 Apr 2015, 05:50
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Bunuel wrote:
What is the probability of rolling three six-sided dice, and getting a different number on each die?

A. 1/12
B. 1/3
C. 4/9
D. 5/9
E. 7/18

Kudos for a correct solution.


6/6 * 5/6 * 4/6
=5/9

Answer: D
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Re: What is the probability of rolling three six-sided dice, and getting a [#permalink] What is the probability of rolling three six-sided dice, and getting a   14 Apr 2015, 09:26
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odds of rolling number on 1 dice is 1/6
odds of rolling another number on 2nd dice is 5/6
odds of rolling a number different from dice 1 and dice 2 on 3rd dice is 2/3
there are 6 total numbers so the resulting probability is
6*1/6*5/6*2/3 =10/18 = 5/9
D
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Re: What is the probability of rolling three six-sided dice, and getting a [#permalink] What is the probability of rolling three six-sided dice, and getting a   14 Apr 2015, 10:04
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1 Possible combinations with three different numbers on each die when three dies are rolled = 6*5*4
2 Total no. of combinations of numbers with three dies = 6*6*6

Divide 1 by 2 and we will get the probability = 6*5*4/6*6*6 = 5/9.

Therefore ans is D.
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Re: What is the probability of rolling three six-sided dice, and getting a [#permalink] What is the probability of rolling three six-sided dice, and getting a   14 Apr 2015, 10:21
Prob of rolling 1st die and getting any number(Lets say x) = 6/6 = 1
Prob 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 = 4/6
Total 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] What is the probability of rolling three six-sided dice, and getting a   09 Oct 2022, 10:03
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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 = \(6^3\) = 216

We 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

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