An appliance wholesaler distributes washing machines made in factories in Akron and Wheeling. Some of these washing machines receive, at customer request, an in-home warranted repair, with the exact breakdown being; Warranted repair No Warranted repair Akron 20 160 Wheeling 50 150 If one the washing machine customers is randomly selected to check on consumer satisfaction, and A is the event that the machine was made in Akron, and R is the event that it had an in-home warranted repair, determine each of the following probabilities: a- P(A) b- P(Rc) c- P(A∩R) d- P(A|R) e- P(AcUR) f- P(Rc|A)
in Statistics Answers by Level 1 User (160 points)

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

The number of Akron machine customers is 160+20=180.

The number of Wheeling machine customers is 50+150=200.

Total number of customers is 180+200=380.

The probability of a random customer being an Akron customer is 180/380=9/19. So the probability of being a Wheeling customer is 1-9/19=10/19 (=200/380). So (a) P(A)=9/19 or 0.4737 or 47.37%.

The meaning of Rc hasn't been defined so I take it to be the complement of R, in other words, the set of customers not having the in-home repair warranty. Similarly, Ac represents the Wheeling customers.

Out of 380 customers, (20+50)=70 took up the offer of the in-home repair, so that's (b) P(R)=70/380, 0.1842 or 18.42%. The probability P(Rc) of no in-home repair warranty is 1-70/380=310/380=0.8158, 81.58%.

(c) The probability of A intersection R, that is, being an Akron customer and having the repair warranty is 20/380=1/19=0.0526, 5.26%.

(d) To find the probability of being an Akron customer or having the warranty, we need to count the customers matching these requirements. 180 Akron customers + 50 Wheeling customers having the warranty=230, so the probability is 230/380=23/38=0.6053, 60.53%.

(e) The total of Wheeling customers, some of whom have the warranty, and Akron customers having the warranty is 200+20=220. This gives the probability 220/380=11/19=0.5789, 57.89%.

(f) 180 Akron customer Service + 150 Wheeling customers with no warranty = 330, making the selection probability 330/380=0.8684, 86.84%.

 

by Top Rated User (982k points)

Related questions

1 answer
asked Oct 9, 2021 in Statistics Answers by Noor Level 1 User (120 points) | 99 views
1 answer
1 answer
asked Mar 24, 2013 in Statistics Answers by Akilie Level 1 User (140 points) | 921 views
1 answer
asked Aug 11, 2014 in Statistics Answers by anonymous | 780 views
2 answers
1 answer
1 answer
asked Aug 17, 2020 in Statistics Answers by anonymous | 409 views
1 answer
asked Jul 13, 2013 in Statistics Answers by Leon89 Level 1 User (160 points) | 842 views
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
86,974 questions
95,835 answers
2,361 comments
24,325 users