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

Answer 1

Answer:  0.6274

Step-by-step explanation:

Given: The proportion of patients experience injection-site reactions with the current needle : p=0.11

Sample size : n= 4

Let x be a binomial random variable that represents the people get an injection-site reaction.

Binomial probability formula: $P(X=x)= ^nC_x p^x(1-p)^{n-x}$

The required probability : P(x=0)

$=\ ^4C_0(0.11)^0(1-0.11)^4\\\\=(1)(1)(0.89)^4\\\\=0.62742241\\\approx0.6274$

Hence, the  probability that none of the 4 people get an injection-site reaction =  0.6274