Question

Question #0325b

Answer 1

1/2

Explanation:

The probability of success in one role is `1/6`
But we have three chances which make it `1/6+1/6+1/6=3/6=1/2`

I answered like the meaning of the question is at lists one.

Answer 2

.347

Explanation:

it is true that the probability of success is 1/6. However in 3 rolls you have the following possible outcomes

success or no success. for each one you have again success or no success and so on. so there are many paths so here are the outcomes

sss
ssn
snn
nnn
nss
nns
nsn
sns

now the ones that have at one success are as follows

snn
nns
nsn
sns

so that would be
`3*1/6(5/6)^2 = .42`

Another approach is to recognize this as a binomial distribution which has the functional form `(""_k^n)p^(k)(1-p)^(n-k)` which in this case is `(""_1^3)1/6(5/6)^2`

In the general case, you always need to consider that there are multiple paths you should take into consideration when dealing with probability.