A salesman normally makes a sale​ (closes) on ​% 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 attempt. ​b) He closes his first presentation on his 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.

Step-by-step explanation:

Given

close

fail to close

First, calculate the value of q

Using complement rule

So, we have:

and

Solving (a): Fails to close on the 4th attempt

This means that he closes the first three attempts. The event is represented as: p p p q

So, we have:

Solving (b): He closes for the first time on the 3rd attempt

This means that he fails to close the first two attempts. The event is represented as: q q p

So, we have:

Solving (c): First he closes is his 2nd attempt

This means that he fails to close the first. The event is represented as: q p

So, we have:

Solving (d): The first he close is one of his 3 attempts

To do this, we make use of complement rule

The event that he does not close any of his first three attempts is: q q q

The probability is:

The opposite is that the first he closes is one of the first three

So, we have:

--- complement rule

2

step-by-step explanation:

1+1=2