If I roll 4 dice, what is the probability that none of the dice showing is a 4?

Question

If I roll 4 dice, what is the probability that none of the dice showing is a 4?

I thought it was (5/6 * 5/6 * 5/6 *5/6) but that is not it.

Can someone explain to me how to get the answer?

Thank you.

Yeah. I misread the answer. Thank you all for the help.

Answer 1

5/6 * 5/6 * 5/6 * 5/6 is the correct answer!

Is it perhaps given in a different form, like
5^4 / 6^4
or
625/1296
or
0.4823
or
48,23%
?

Maybe you misread the question?

Maybe the dice are not fair and there is a higher possibility that a dice shows say 1 or 3 than 2, 4, 5 or 6.

It is also possible that the answer given in the book is incorrect.

Answer 2

I think this is the answer you were looking for:-
With 4 6-sided dice there are a total of 1296 (6*6*6*6) different permutations that can they can land in.
The number of those permutations that contain a 4 are 864 (1*6*6*6 + 6*1*6*6 + 6*6*1*6 + 6*6*6*1 or 216*4).
Therefore there are a total of 432 (1296-864) permutations that do not contain a 4.
So the answer is 432/1296=1/3.

Further thought we have to exclude duplicate permutations meaning there are 671 permutations containing a 4 therefore 625 that do not contain a 4, so 625/1296=0.482253086.

The number of permutations that contain a 4 (and excluding duplicates) are 671 (1*6*6*6 + 5*1*6*6 + 5*5*1*6 + 5*5*5*1 = 216+180+150+125 = 671)
Therefore there are 625 (1296-671) permutations that do not include a 4.
So the answer is 625/1296=0.482253086 = 5/6 * 5/6 * 5/6 * 5/6.

Answer 3

The answer to your first question: 48.2253% is the probability that none of the 4 dice you roll will show a 4.
You could round this answer to 48.23% if need-be.
TO VERIFY 48.2253% by using only 11 keystrokes please see the end of my reply.

The answer to your second question is as follows:
We must determine how many chances there are that
any number but 4 will show in relation to the total number
of chances of all 6 numbers.

You have four dice, each having the probability that
4 will not show 5 of 6 times rolled. We now know that
5*5*5*5 will tell us the total number of non number 4
chances.

We also now know that 6*6*6*6 will tell us the total number
of all chances, including the number 4.

Formula>(5/6*5/6*5/6*5/6)*100 = probability no 4 shows
after rolling 4 dice

(5/6*5/6*5/6*5/6) = 625/1296
625/1296 = .482253 *100 = 48.2253%

TO VERIFY 48.2253% as the correct answer:
On your calculator: Divide 5 by 6, press =, then
press X square key twice, multiply by 100, press =
to conclude.

Answer 4

Probability that a dice does not show a 4 = 5/6
So I would have thought that probability of 4 dies not showing a four is (5/6).(5/6).(5/6).(5/6)
= 625/1296

Answer 5

there are 6 numbers that u can get for each dice. and u have 4 of them. so that means u have a possiblity of 24 numbers. and u don't want to get 4. and u only have 4 4's cause there is only one 4 for each dice. so 4/24 = 1/6. so the possiblity of getting 4 is 1/6 and the possibility of not getting 4 is 20/24 which reduces to 5/6.

Answer 6

4x6=24 the four is the number of dice 6 is how many numbers now you see that there is 24 so you need to make this a fraction 1/6x3= 3/6 now u need to make 3/6 with a denomatior of 24 so your answer is 4/24

Answer 7

If the 4 dice are fair dice, you're answer is correct.
The only reason you're answer is incorrect is if the dice are "unfair" or "loaded" dice.

Answer 8

50/50 either you will or you wont.