Answer :
The given statement is a reasonable probability model because it fulfills the 4 conditions of binomial distribution.
How to identify binomial distribution model?
The conditions for binomial distribution are;
1: The number of observations n must be fixed.
2: Each observation must be independent.
3: Each observation must represent one of two outcomes ("success" or "failure").
4: The probability of "success" p must be the same for each outcome.
Now, we are given the statement;
Joey buys a Virginia lottery ticket every week. x is the number of times in a year that he wins a prize.
From that statement, we can tell that the number of observations is fixed at 52 weeks since a year is made up of 52 weeks.
Secondly, we can say that there could be success by winning a price or failure by not winning the price.
Each weekly observation is independent.
The probability is the same for each outcome.
Thus, we conclude that since it fulfills all the four conditions then it is a binomial model.
Read more about Binomial distribution at; https://brainly.com/question/15246027
#SPJ1