Question

A vasectomy is​ 99.97% effective, with pregnancy occuring extremely rarely after the 3 month wait​ period, once the procedure is complete. A doctor claims to have performed​ 8,303 vasectomies in his career.​ (Round to 2 decimal​ places)
​a) What is the likelyhood that at least one of the vasectomies performed was not​ effective? (Answer in​ Percent)

nothing​%

​b) What is the Expected Number of failed vasectomies performed by the​ doctor?

8300.51

​c) What is the Expected Number of vasectomies performed before a patient returns complaining that his was not​ effective?

nothing

​d) Find the probability that 0 of his patients had a failed vasectomy.​ (Answer in​ Percent)

nothing​%

​e) Find the probability that the 2nd person he performed a vasectomy on was the first person on which he performed it successfully.​ (Answer in​ Percent)

nothing​%

Answer 1

Answer:

Required probability  = 91.72%

expected number = 2.4909

Expected number = 3332.33

probability = 8.28%

Required probability = 0.03%

Explanation:

given data

effective = 99.97%

time = 3 month

claims performed​ = 8,303

solution

At least one of the vasectomies perform not​ effective

so Required probability = 1 - P(All are effective)     .................1

put here value and we get

Required probability  = $1 - (0.9997)^{8303}$      

Required probability  = 1 - 0.0828

Required probability  = 0.9172

Required probability  = 91.72%

and

we know expected number is express as here

expected number is = n × p     ..................2

put here value and we get

expected number = 8303 × (1 - 0.9997)

expected number = 8303 × 0.0003

expected number = 2.4909

and

Expected Number of vasectomies perform before patient return complain is

Expected number =   $\frac{1}{p} - 1$       ..............3

put here value and we get

Expected number =  $\frac{1}{(1-0.9997)} - 1$  

Expected number = 3333.33 - 1

Expected number = 3332.33

and

when probability that 0 of his patients

probability = 100% - 91.72%

probability = 8.28%

and

when probability that the 2nd person he performed a vasectomy than

Required probability = p × q     ...................4

put here value and we get

Required probability = (1-0.9997) × 0.9997

Required probability = 0.0003

Required probability = 0.03%