Step 1 :This problem is about the binomial distribution. The binomial distribution model deals with finding the probability of success of an event which has only two possible outcomes in a series of experiments. For a random variable X if n is the number of experiments, p is the probability of success in a single experiment, then the probability mass function of X is given by: \(P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))\), where \(C(n, k)\) is the combination of n items taken k at a time.
Step 2 :In this case, \(n=27\) (the number of purchases), \(p=0.152\) (the probability of winning a prize), and we want to find \(P(X=4)\), the probability of winning 4 prizes.
Step 3 :Substituting the given values into the formula, we get: \(P(X=4) = C(27, 4) * (0.152^4) * ((1-0.152)^(27-4))\).
Step 4 :Calculating the above expression, we get a probability of approximately 0.211.
Step 5 :Final Answer: The probability that you win 4 prizes is approximately \(\boxed{0.211}\).