Question

Roll a six-sided die 8 times. What is the probability that 6 will appear at least 5 times?

Answer 1

five 6's in only 8 rolls is pretty difficult

Answer 2

indeed

Answer 3

the probability of rolling a certain number in a single role is 1 out of 6

Answer 4

Say that happens on first role,

the probability for the next roll is the same, 1/6
and for all 8 rolls the same

Answer 5

k

Answer 6

to get 5 of those you need that 1/6 to happen 5 times

1/6 * 1/6 * 1/6 * 1/6 * 1/6

Answer 7

1/7776

Answer 8

yeah,. that is for rolling all in a row...

Answer 9

the change of not getting 6 is 5/6 for each roll

Answer 10

ok

Answer 11

so above we considered 5 rolls , want 8 total rolls
the 3 left can be misses with a 5/6 chance

Answer 12

so 5 times chance of getting 6 + 3 times chance of missing is getting 'at least' five sixes out of 8 rolls

Answer 13

[1/6 ]^5 * [5/6] ^3

Answer 14

in other word is 5(9)?

Answer 15

8 rolls total. multiply the probability for each one together. 5 of them should be 1/6 and 8 of them should be 5/6

Answer 16

i got like 125/1679616

Answer 17

ok

Answer 18

yeah , small chance

Answer 19

do that mean i need to add 5,6,7,and 8?

Answer 20

that fraction is about 0.00007

Answer 21

that number is too long

Answer 22

perhaps im wrong

Answer 23

were you shown the formula with the n and k , n rolls , k times something occurs

Answer 24

\[\left(\begin{matrix}n \\ k\end{matrix}\right) p^k(1-p)^{n-k}\] this formula ?

Answer 25

that looks good

if you see, it is the same thing we did above

Answer 26

p = success chance, so (1-p) is the chance of fail
k = # success
n = # failed


p=1/6 , (1-p) = 5/6
k= 5 rolls
n = 3 rolls

Answer 27

ok got 0.00461

Answer 28

That is correct.

Answer 29

k thx so much

Answer 30

You're welcome :)