.
Two computers A and B are to be marketed. A salesman who is assigned the job of finding customers for them has 70% and 30%
chances respectively of succeeding in case of computer A and B. The computers can be sold independently.
Given that he was able to sell at least one computer, what is the probability that the computer A has been sold?
~~~~~~~~~~~~~~~~~~~~~~~~~~~
The key to solving this problem is hidden in THIS phrase
The computers can be sold independently.
Actually, in the hidden form, this phrase represents the following statement:
The probability to sell both computers simultameously P(A and B) is the product P(A) and P(B):
P(A and B) = P(A)*P(B).
Having it deciphered, we are in one step from the solution.
1) The probability that at least one computer is sold is
P(A and B) = P(A) + P(B) - P(A and B) = P(A) + P(B) - P(A)*P(B) = 0.7 + 0.3 - 0.7*0.3 = 1 - 0.21 = 0.79.
2) The probability that the computer A has been sold given that at least one computer was sold is this CONDITIONAL probability
P(A sold | at least one of A or B was sold) = = = 0.886 = 88.6%. ANSWER
Solved.
--------------
To see many other solved problem on CONDITIONAL probability and to learn this complicated subject BETTER, WIDER and DEEPER,
look into the lessons
- Conditional probability problems
- Conditional probability problems REVISITED
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Solved problems on Probability"
and "Additional problems on Probability".
Save the link to this textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.