I came with this question solving a programming problem, but my question is math related.
The problem is a bowling system which the wording of the question says:
The application will randomly choose the number of pins knocked down, with a double chance to the pins $7,8,9$ and $10$.
So the pins $1$ to $6$ have a chance of $1/2$ to be knocked down.
So I came with something like this:
if random(0 ~ 100) < 50 => pin dropped
And my first thought of what would be a "double chance" was $2/3$.
if random(0 ~ 100) < 66 => pin dropped
But after writing it down I realized that the difference of the pins $1$-$6$ to pins $7$-$10$ was less than I though, just $15\%$ greater. So I started wondering if I may be misinterpreting the question.
I was thinking if a probability of two consecutive $1/2$ could be $(1/2)^2 = 25\%$ and $75\%$
I may be totally wrong, I need a second though on this.