Imagine we're rolling $3$ dice. How many times do we need to roll them so we get a sum of $15$ with a probability of $0.6$?
What I got so far:
We're throwing the dices $n$ times (this hints at Bernoulli trials...?)
The event we're watching is:
$A$: the sum of the rolled numbers is $15$
We have that the probability of $P_n(A) = 0.6$
There're $10$ combinations to get a sum of $15$. How do I proceed?
The probability of rolling a $15$ is $\frac5{108}$. The probability of not rolling a $15$ after $n$ rolls would be $$ \left(\frac{103}{108}\right)^n $$ Thus, the probability of rolling a $15$ within the first $n$ rolls is $$ 1-\left(\frac{103}{108}\right)^n $$ Find the $n$ so that this is greater than $0.6$.