a medical device company knows that 12% of patients experience injection - site reactions with the current…
a medical device company knows that 12% of patients experience injection - site reactions with the current needle. if 6 people receive injections with this type of needle, what is the probability that at least one of them has an injection - site reaction?\n0.0633\n0.4644\n0.5356\n0.7200
Answer
Explanation:
Step1: Find probability of no reaction
The probability that a single - patient has no injection - site reaction is $1 - 0.12=0.88$. Since the events of each patient not having a reaction are independent, for 6 patients, the probability that none of them has a reaction is $(0.88)^6$. $(0.88)^6=0.88\times0.88\times0.88\times0.88\times0.88\times0.88\approx0.4644$.
Step2: Find probability of at least one reaction
The probability that at least one patient has a reaction is the complement of the event that none of them has a reaction. Let $P(X\geq1)$ be the probability that at least one patient has a reaction and $P(X = 0)$ be the probability that none of the patients has a reaction. Then $P(X\geq1)=1 - P(X = 0)$. $P(X\geq1)=1-(0.88)^6\approx1 - 0.4644 = 0.5356$.
Answer:
0.5356