Question

2) A salesman normally makes a sale​ (closes) on 60​% of his presentations. Assuming the presentations are​ independent, find the probability of the following.

​a) He fails to close for the first time on his sixth attempt.

​b) He closes his first presentation on his fifth attempt.

​c) The first presentation he closes will be on his second attempt.

​d) The first presentation he closes will be on one of his first three attempts

. ​a) ​P(X=6​)=____​(Round to four decimal places as​ needed.)

​b) ​P(X=5)=____​(Round to four decimal places as​ needed.)

​c) ​P(X=2)=____​(Round to four decimal places as​ needed.) ​

d) The probability the first presentation he closes will be on one of his first three attempts is______ .​(Round to four decimal places as​ needed.)

Answer 1

P(closes on an attempt)= 0.60

P(fails to close) = 1 - 0.60 = 0.40

a) P(fails to close for the first time on his sixth attempt) = P(closes on first 5 attempts) x P(fails to close on 6th attempt)

= 0.6⁵ x 0.4

= 0.0311

b) P(closes his first presentation on his fifth attempt) = P(fails to close on first 4 attempts) x P(closes on fifth attempt)

= 0.40⁴ x 0.60

= 0.0154

c) P(first presentation he closes will be on his second attempt) = P(fails to close on first attempt) x P(closes on second attempt)

= 0.4 x 0.6

= 0.24

d) P(first presentation he closes will be on one of his first three attempts) = 1 - P(first presentation he closes will not be on one of his first three attempts)

= 1 - P(fails to close on first 3 attempts)

= 1 - 0.4³

= 0.936