Question

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If Greg rolls four dice, what is the probability that he rolls more 1's than 6's?

Answer 1

okay

Answer 2

u know what will be the individual probability??

Answer 3

What is that?

Answer 4

like if u roll one dice

Answer 5

what is the probablity if u roll one dice for the given constraints?

Answer 6

If you roll one dice, then you can't have more. There's only one number to base it on.

Answer 7

first find prob of rolling 1

Answer 8

then prob of rolling 6

Answer 9

1/6

Answer 10

I am little rusty in probability...hold on

Answer 11

1 dice - probability of any number is 1/6
4 dices - probability of any number is 4/6
so the probability is the same for any number

Answer 12

Does this mean that the probability is 4/6?

Answer 13

@Fallontine it says how many more 1s than 6s??

Answer 14

how do u interpret that??

Answer 15

ammm... wait...

Answer 16

ok..:)

Answer 17

this is a permutation

Answer 18

oh......so how did u proceed??

Answer 19

prob of finding 1=1/6
of finding 6=5/6

Answer 20

for one dice

Answer 21

noooo... it's 1/6 for 1, 1/6 for 2 etc... and 1/6 for 6 coz you have 6 numbers and you have to choose 1 and the probability is the same for all of them

Answer 22

I know, what permutation is this??

Answer 23

Wait, can't we do casework?

Answer 24

We can consider the various cases where there are more ones than sixes
- one dice with a 1 and no dice with 6s
- two dice with 1s and no dice with 6s
- two dice with 1s and one dice with 6
- three dice with 1s and no dice with 6s
- three dice with 1s and one dice with 6
- four dice with 1s

Answer 25

no no after u have chosen 1/6 for 1 6 can be anywhere in the rest 5 numbers hence 5/6

Answer 26

Is that right??

Answer 27

@Fallontine

Answer 28

Hello? :)

Answer 29

it seems you just need to find how many ways the outcome can have more 1s than 6s and divide that by the total number of possible outcomes

Answer 30

Oh yeah! Just a sec while I figure it out.

Answer 31

1111 1116 1161.....like that

Answer 32

@TuringTest Thank u .I got it

Answer 33

How many possible outcomes are there? @TuringTest

Answer 34

1116, 1161, 1611, 6111, 1111
five outcomes with more 1s than 6s

Answer 35

I mean the number in the denominator.

Answer 36

well how many total ways can one throw the dice?
there are 6 possible outcomes for the first die
6 outcomes for the second die, etc

Answer 37

Oh, so 6^4

Answer 38

when you flip a coin, the number of different outcomes you can get is 2^n where n is the number of flips
yep :)

Answer 39

you also have to count with the other numbers (2 to 5)
there are many many possibilities with no 1 or 6 at all

Answer 40

indeed, I forgot to count 11x6, 1xxx, and so on
my mistake