What is the probability of rolling a dice 3 times and getting different number each time?


What is the probability of rolling a dice 3 times and getting different number each time?

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What is the probability of rolling three six-sided dice, and getting a [#permalink]

What is the probability of rolling a dice 3 times and getting different number each time?
  14 Apr 2015, 04:14

What is the probability of rolling a dice 3 times and getting different number each time?

What is the probability of rolling a dice 3 times and getting different number each time?

00:00

Question Stats:

What is the probability of rolling a dice 3 times and getting different number each time?
81% (01:33) correct
What is the probability of rolling a dice 3 times and getting different number each time?
19% (02:05) wrong
What is the probability of rolling a dice 3 times and getting different number each time?
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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

Kudos for a correct solution.

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Posts: 86975

What is the probability of rolling three six-sided dice, and getting a [#permalink]

What is the probability of rolling a dice 3 times and getting different number each time?
  20 Apr 2015, 05:26

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 a dice 3 times and getting different number each time?
  14 Apr 2015, 04:29

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 a dice 3 times and getting different number each time?
  14 Apr 2015, 04:50

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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Posts: 108

Re: What is the probability of rolling three six-sided dice, and getting a [#permalink]

What is the probability of rolling a dice 3 times and getting different number each time?
  14 Apr 2015, 08:26

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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Posts: 191

Re: What is the probability of rolling three six-sided dice, and getting a [#permalink]

What is the probability of rolling a dice 3 times and getting different number each time?
  14 Apr 2015, 09:04

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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Posts: 51

Re: What is the probability of rolling three six-sided dice, and getting a [#permalink]

What is the probability of rolling a dice 3 times and getting different number each time?
  14 Apr 2015, 09:21

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 a dice 3 times and getting different number each time?
  09 Oct 2022, 09:03

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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Re: What is the probability of rolling three six-sided dice, and getting a [#permalink]

09 Oct 2022, 09:03

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What is the probability of a dice rolling a 3?

To understanding probability we take an example as rolling a dice: There are six possible outcomes—1, 2, 3, 4, 5, and 6. The probability of getting any of the numbers is 1/6. As the event is an equally likely event so the possibility of getting any number is the same in this case it is 1/6 or 50/3%.

How many ways can 3 dice of different colors be thrown at the same time?

This approach yields a list of numbers. We can list all possible outcomes for the three dice and add a fourth column that contains a 0 if the event is not in A and contains a 1 if the event is in A. By simple counting, we find that there are 15 outcomes in event A, out of the total of 216 possible outcomes.