Question

2) Assume that the probability of success rate for a surgical procedure is 0.95.

a) What is the probability that three surgeries are successful?

b) What is the probability that none of the three surgeries are successful?

c) What is the probability that of the three surgeries, at least one surgery is successful?

**I haven't learned any of the equations generally used to solve these problems so a common way to solve would be appreciated!!

Answer 1

The probability of success rate for a surgical procedure is 0.95.

Since all the surgeries are mutually exclusive we know that

a) probability that three surgeries are successful = p^3 =0.95^3 (Negative Binomial Distribution of probabilities)

=0.857375

b) Same as above the probability that none of the three surgeries are successful = (1-p)^3 =0.05^3 = 0.000125

c) The probability that of the three surgeries, at least one surgery is successful

= exactly 1 successful surgery +exactly 2 successful surgery+exactly 3 successful surgery

=0.95*0.05^2 + 0.95^2*0.05 + 0.95^3

=0.904875

Hope the above answer has helped you in understanding the problem. Please upvote the ans if it has really helped you. Good Luck!!