The article “Checks Halt over 200,000 Gun Sales” (San Luis Obispo Tribune, June 5, 2000) reported that required background checks blocked 204,000 gun sales in 1999. The article also indicated that state and local police reject a higher percentage of would be gun buyers than does the FBI, stating, “The FBI performed 4.5 million of the 8.6 million checks, compared with 4.1 million by state and local agencies. The rejection rate among state and local agencies was 3%, compared with 1.8% for the FBI.”
a. Use the given information to estimate P(F), P(S), P(R| F), and P(R| S), where F = event that a randomly selected gun purchase background check is performed by the FBI, S = event that a randomly selected gun purchase background check is performed by a state or local agency, and R = event that a randomly selected gun purchase background check results in a blocked sale.
b. Use the probabilities from Part (a) to create a “hypothetical 1000” table. Use the table to compute P(S| R), and write a sentence interpreting this value in the context of this problem. Additional Exercises