Researchers studied the antimicrobial resistance of N.gonorrhoeae, the bacteria responsible for gonorrhea. Isolates ofthe bacteria were obtained from a large sample of patients who werediagnosed with gonorrhea. An isolate of N. gonorrhoeae is resistantto penicillin (event A) with probability .128, is resistant totetracycline (event B) with probability .204, and is resistant toboth penicillin and tetracycline (A and B) with probability .104.(The probabilities .128 and .204 both include the probability.104.)
a) Use the complement rule to find the probability that an isolateis not resistant to penicillin.
b) Use the general addition rule to find the probability that anisolate is resistant to penicillin or to tetracycline.
c) Find the probability that an isolate is resistant to penicillinbut not to tetracycline.
d) First give the mathematical notation for the conditionalprobability that an isolate is resistant to penicillin given thatit is
resistant to tetracycline, and then calculate that conditionalprobability. Give it to 4 decimal places.
Researchers studied the antimicrobial resistance of N.gonorrhoeae, the bacteria responsible for gonorrhea. Isolates ofthe bacteria were obtained from a large sample of patients who werediagnosed with gonorrhea. An isolate of N. gonorrhoeae is resistantto penicillin (event A) with probability .128, is resistant totetracycline (event B) with probability .204, and is resistant toboth penicillin and tetracycline (A and B) with probability .104.(The probabilities .128 and .204 both include the probability.104.)
a) Use the complement rule to find the probability that an isolateis not resistant to penicillin.
b) Use the general addition rule to find the probability that anisolate is resistant to penicillin or to tetracycline.
c) Find the probability that an isolate is resistant to penicillinbut not to tetracycline.
d) First give the mathematical notation for the conditionalprobability that an isolate is resistant to penicillin given thatit is
resistant to tetracycline, and then calculate that conditionalprobability. Give it to 4 decimal places.
