Question 1181566
.
Find the indicated probabilities using the geometric​ distribution, the Poisson​ distribution, or the binomial distribution. 
Then determine if the events are unusual. If​ convenient, use the appropriate probability table or technology 
to find the probabilities.
Assume the probability that you will make a sale on any given telephone call is 0.13. Find the probability that you​ 
(a) make your first sale on the fifth​ call, 
(b) make your sale on the​ first, second, or third​ call, and​ 
(c) do not make a sale on the first three calls.
~~~~~~~~~~~~~~~~~~~



<pre>
(a)  "First sale is on the fifth calls"  MEANS  that 4 first trials were unsuccessful, and the 5th trial was successful


        P = {{{(1-0.13)^4*0.13}}} = 0.0745 = 7.45%   (rounded).    <U>ANSWER</U>




(b)  "make your sale on the​ first, second, or third​ call"  means that SOME one of the 3 trials was successful, 

     while two other trials were unsuccessful.  In this interpretation, it is classic BINOMIAL distribution problem


        P = {{{C[3]^1*0.13*(1-0.3)^2}}} = {{{3*0.13*0.87^2}}}  = 0.2952 = 29.52%   (rounded).      <U>ANSWER</U>     (see my comment at the end of my post)




(c)  "do not make a sale on the first three calls"   MEANS that these tree 3 trials were all unsuccessful


        P = (1-0.13)*(1-0.13)*(1-0.13) = {{{(1-0.13)^3}}} = {{{0.87^3}}} = 0.6585 = 65.85%   (rounded).    <U>ANSWER</U>    
</pre>


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;@greenestamps was right noticing my error in part &nbsp;(b) &nbsp;&nbsp;(I misread the problem) - - - thanks for it.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;After getting his note, &nbsp;I changed this part and fixed this fault.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Now you see the corrected version there.



/\/\/\/\/\/\/\/



The problem is just solved - - - all the questions are answered and explained.


------------



Happy learning &nbsp;(!)



Do not forget to post your &nbsp;"THANKS" &nbsp;to me for my teaching.