A new surgical procedure is said to be successful 80% of the time. Suppose that theoperation is performed five times, with the results being independent of each other. Weare interested in the successfulness of this operation.(a) Define an appropriate random variable X for this problem.

A new surgical procedure is said to be successful 80% of the time. Suppose that theoperation is performed five times, with the results being independent of each other. Weare interested in the successfulness of this operation.(a) Define an appropriate random variable X for this problem.(b) What particular type of distribution does the random variable X have? State thevalues of the parameters.Find the following probabilities:(c) Exactly three operations are successful.(d) Fewer than two operations are successful.(e) More than three are successful.

A new surgery is successful 80% of the time. If the results of 8 such surgeries are randomly sampled, what is the probability that more than 5 of them are successful?Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places.(If necessary, consult a list of formulas.)

Two hundred patients who had either hip surgery or knee surgery were asked whether they were satisfied or dissatisfied regarding the result of their surgery. Out of the 95 that had knee surgery, 70 were satisfied. Out of the 105 that had hip surgery, 15 were dissatisfied. If one person from the 200 patients is selected at random, what is the probability that the person had knee surgery?Question 4Select one:a.5/19b.21/40c.7/20d.19/40

X can solve 80% of the problems while Y can solve 90% of the problems given in a statistics book.A problem is selected at random. What is the probability that at least one of them will solve thesame?

B. How many of the outcomes are favorable?