Question

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? 0.0633 0.4644 0.5356 0.7200

Explanation:

Step1: Calculate the probability of no reaction

The probability of a patient not having a reaction is \(1 - 0.12=0.88\).
For \(n = 6\) independent patients, the probability that none of them has a reaction is \(P(X = 0)=0.88^{6}\).
Using a calculator, \(0.88^{6}\approx0.4644\).

Step2: Use the complement rule

The probability that at least one has a reaction is \(P(X\geq1)=1 - P(X = 0)\).
Substitute \(P(X = 0)\approx0.4644\) into the formula: \(P(X\geq1)=1 - 0.4644 = 0.5356\).

Answer:

0.5356