Question 664071
.
I am a salesperson & I close on 70% of all my sales. If I call on 4 sales, what is the probability 
that I will close on 3 of the 4 sales?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~



        In the post by @Theo, there are too many words and too many excessive calculations.

        It is not a mathematical style solving and not a good style teaching.

        I came to provide a solution in the form as it should be done and presented.



<pre>
This problem is on Binomial distribution.

The number of trials is 4.  The probability of a success at each individual trial is p = 0.7.

They want you find the probability of having 3 success in 4 trials.


Use the formula for binomial distribution


    P(n=4; k=3; p=0.7) = {{{C(4,3)*p^3*(1-p)^1}}},


where  C(4.3) = {{{4!/3!}}} = {{{(1*2*3*4)/(1*2*3)}}} = 4 is the binomial coefficient.

The formula gives

    P = {{{4*0.7^3*0.3}}} = 0.4116.


<U>ANSWER</U>.  The probability to close 3 sales of 4 sales in this problem is 0.4116.
</pre>

Solved.


As you solve your problems on Binomial distribution, when you treat this given problem 
among many others problems of this topic, two moments are important: 


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(a) &nbsp;to recognize from the text that this given problem is on Binomial distribution, 


&nbsp;&nbsp;&nbsp;&nbsp;and


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(b) &nbsp;to apply an appropriate formula of the binomial distribution.


These are the key. &nbsp;&nbsp;The rest is pure mechanical job for a calculator.