Question 5
Determined to crack down on the drug trade, a city mayor puts more officers out on patrol to disrupt the business of drug dealers. A drug dealer in a neighborhood can work his trade either on a street corner or in the park. Each day, he decides where to set up shop, knowing that word about his location will travel among users. Because a good snitch is lacking, word does not travel to the police. The police officer on the beat then needs to decide whether she will patrol the park or the street corner, while not knowing where the drug dealer is hanging out that day. The decision of the officer and the dealer determine the extent of drug trades that day. Let suppose the total number of potential trades in the market is 100. A dealer's payoff is determined by the number of trades he consummates, while the officer’s payoff is based on the number of trades she disrupts. The table below illustrates the payoffs for both parties according to their respective strategies in the game.
Based on the above data, answer the given subquestions.
If the randomization probability of a police officer for patrolling the streets is p/13, then p =__________