97% of Dr. William’s patients end up with 20-30 vision or better. Find the probability that exactly 3 of her next patients end up with 20-30 vision or better.
Assuming the events are independent, than the probability of obtaining exactly x successes, P(x), in n independent trails is given by P(x) = (nCx) pxqn-x where p is the probability of success on a single trial and q is the probability of failure on a single trial.
We will consider a ‘success’ a patient ending with 20-30 vision or better.
The probability the patient’s vision is a success is 0.97.
The probability the patient’s vision is a failure is thus 1 – 0.97, or 0.03.
Thus, n = 4, x = 3, p = 0.97, and q = 0.03.
Substitute the values.
P(3) = (4C3)(0.97)3(0.03)1