Question

a medical device company knows that 11% of patients experience injection - site reactions with the current needle. if 4 people receive injections with this type of needle, what is the probability that none of the 4 people get an injection - site reaction? 0.0001 0.3726 0.4400 0.6274

Explanation:

Step1: Calculate the probability of no reaction for one person

The probability of a patient having an injection - site reaction is \(p = 0.11\). So the probability of a patient not having an injection - site reaction is \(q=1 - p=1 - 0.11 = 0.89\).

Step2: Use the multiplication rule for independent events

Since the events (each person not having a reaction) are independent, for \(n = 4\) people, the probability that none of them have a reaction is \(q\times q\times q\times q=q^{n}\).
Substitute \(q = 0.89\) and \(n = 4\) into the formula: \(P=(0.89)^{4}\).
Calculate \((0.89)^{4}=0.89\times0.89\times0.89\times0.89 = 0.6274\) (rounded to four decimal places).

Answer:

0.6274