4 shots are fired from an army tank to completely blast an enemy car. Each shot has 3 possible outcomes - blast the car, damage it or miss it. 2 damaging shots blast the car. Find the probability that the car is blasted.
Shots that blast it and damage it are taken separately as in shots that blast also damage need not be considered.
I understand the total possible outcomes are 3^4 = 81, and have no idea how to proceed further. Help pls.
HINT
Let's make a simplifying assumption that the shot results are independent from the results of other shots. Let's set the probability to miss in any shot as $p$ and the probability to damage as $q$, so the probability to blast will be $1-p-q$.
Now, the only way to not blast the enemy car is to damage it once in $n=4$ attempts, or not to damage it at all, i.e., miss all 4 times. The probability to miss all times is $p^n$. The probability to damage once is given by $$\binom{n}{1} p^{n-1} q = np^{n-1}q,$$ so what would the final probability be?