Expert: Sherry Wallin - 8/19/2010

Question
Hi,
Below is the problem of probability,a request  for solution
Q. Two Vaccum cleaner Sales man A & B must each make two
calls per day, one in the morning & one in afternoon . 'A'
has probability of 0.4 of selling a cleaner on any call,
while 'B' has probability 0.1 of a sale. 'A' works
independently independently of 'B' and for each salesman
morning and afternoon result are independent of each other,
find the probability that in one day:
1. 'A' sells two cleaners
2. 'A' sells just one cleaner
3. 'B' makes atleast one sell
4. Between then 'A' & 'B' make exactly one sell

Answer
N = no sale Y = sale
Call A sells two cleaners event C
The sample space is:
NN = .6(.6) = .36
NY = .6(.4) = .24
YN = .4(.6) = .24
YY = .4(.4) = .16
P(C) = .16 since there is only one way in the sample space for C to occur

There are two out of four ways for A to sell just one cleaner, call this event D.
P(D) = .24 + .24 = .48  

P(B) makes at least one sell is the same as the probability B sells 1 or 2, call this event E: Salesman B has a sample space of:

NN =.9(.9) = .81
NY = .9(.1) = .09
YN = .1(.9) = .09
YY = .1(.1) = .01
There are 3 out of 4 ways Salesman B can sell at least one cleaner thus

P(E)= # of ways E can occur/number of different simple events for B
= .09 + .09 +.01 = .19

To make exactly one sale means you have to exclude NN and YY from both sample spaces for A and B

P(C or D) = .24 + .24 + .09 + .09 = .68

Math Prof