Question

You roll a die 4 times, if it's 1 to 5 score 0, else a 6 scores 1.

The total score is the sum of the 4 scores.

Find the probability of a total score of 3.

Answer 1

the ways to get 3:
0, 1, 1, 1
1, 0, 1, 1
1, 1, 0, 1
1, 1, 1, 0

Answer 2

(1/6)(1/6)(1/6)(5/6)

Answer 3

that times 4

Answer 4

(1/6)(1/6)(1/6)(5/6)+(1/6)(5/6)(1/6)(1/6)....

Answer 5

I think the four rolls is already accounted for in my answer.

Answer 6

No. You only accounted for one way to get 3 from 4 rolls

Answer 7

5/324 is correct

Answer 8

Each roll is a Bernouilli trial and the outcomes have a binomial distribution.

Answer 9

ohh lol I forgot all about Bernoulli's trials.. I just used:
1, 1, 1, 0 -> (1/6)(1/6)(1/6)(5/6)
1, 1, 0, 1 -> (1/6)(1/6)(5/6)(1/6)
1, 0, 1, 1 -> (1/6)(5/6)(1/6)(1/6)
0, 1, 1, 1 -> (5/6)(1/6)(1/6)(1/6)
You could have either of those rolls. So you add the probabilites up

Answer 10

So P(s) = 4!/s!(4-s)! * (1/6)^s(5/6)^(4-s)

Answer 11

Thats 4 rolls 4 times isn't it bahrom?

Answer 12

yea it is @pantsmaster but there are 4 ways to get a 3 from 4 rolls

Answer 13

\[ \binom{4}{1} \left( 1 \over 6\right)^{4-1}\left(5 \over 6 \right)^1 \text{ or equivalently } \binom{4}{3} \left( 1 \over 6\right)^{4-1}\left(5 \over 6 \right)^1\]

Answer 14

Yikes, I'm in trouble for my Stats/prob test coming up then lol

Answer 15

:-)