Question

A vasectomy is​ 99.97% effective, with pregnancy occurring 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 likelihood that at least one of the vasectomies performed was no effective?

b. what is the expected number of failed vasectomies performed by the doctor?
c. what is the expected number of vasectomies performed before a patient returns complaining that his was not effective?

b. find the probability that 0 of his patients had a failed vasectomy.

find the probability that the 2nd person he performed a vasectomy on was the first person on which he performed it successfully

Answer 1

Answer:

a)

Required probability = 1 - P(All are effective)

= 1 - (0.9997)^8303

= 1 - 0.0828

= 0.9172

= 91.72%

b)

Now expected number = np

substitute values

= 8303*(1 - 0.9997)

= 8303*0.0003

= 2.4909

c)

Expected number = 1/p - 1

substitute values

= 1/(1-0.9997) - 1

= 3333.33-1

= 3332.33

d)

Proability = 100% - 91.72%

= 8.28%

e)

Required probability = pq

substitute values

= (1-0.9997)*0.9997

= 0.0003

= 0.03%