The probability of at least 1 occurrence though is
p = 1 - (1 - .027)^16 -> that's about 0.35
Where do you get 16/36 from ?
16/36 is the Expectancy. for independent events E(nX) = n*E(X)
Let {\displaystyle X}
be a random variable with a countable set of finite outcomes {\displaystyle x_{1}}
, {\displaystyle x_{2}}
, ..., occurring with probabilities {\displaystyle p_{1}}
, {\displaystyle p_{2}}
, ..., respectively, such that the
infinite sum {\displaystyle \textstyle \sum
{i=1}^{\infty }|x{i}|\,p_{i}}
converges. The expected value of {\displaystyle X}
is defined as the series
{\displaystyle \operatorname {E} [X]=\sum
{i=1}^{\infty }x{i}\,p_{i}.}
What you have calculated is the p >=1 event occuring