Probability: The Law of Total probability and Bayes' rule

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Question 1:
Last year, a new business purchased 25 tablets, 25 laptops, and 50 desktops, all with three year warranties. The probability a tablet has had warranty work is four times the probability a desktop has had warranty work. The probability a laptop has had warranty work is twice the probability a desktop has had warranty work. Given that 10 computers have used the warranty, (a) If a computer is a laptop, what is the probability it has had warranty work? (b) If a computer has had warranty work, what is the probability it was a laptop? (c) If a computer has had warranty work, what is the probability it was a tablet?



Question 2:
The products of an agricultural firm are delivered by four different transportation companies, A, B, C and D. Company A transports 40% of the products; company B, 30%; company C, 20%; and finally, company D, 10%. During transportation, 5%, 4%, 2%, and 1% of the products spoil with companies A, B, C, and D, respectively. If one product is randomly selected, (a) Obtain the probability that it is spoiled. (b) If the chosen product is spoiled, derived the probability that it has transported by company A.



Question 3:
A salesman in a department store receives household appliances from three suppliers: I, II and III. From previous experience, the salesman knows that 2%, 1%, and 3% of the appliances from suppliers I, II, and III, respectively, are defective. The salesman sells 35% of the appliances from supplier I, 25% from supplier II, and 40% from supplier III. If an appliance randomly selected is defective, find the probability that it comes from supplier III.




probability




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    These are three questions in one post, you better split it up in separate entries. In addition, show some effort of yourself. This site is not meant to provide you an answer just like that.
    – Nicky Hekster
    Jul 30 at 11:02






  • 1




    As you are new to the site: people here tend to not respond well (or at all) to questions like these that look like routine homework problems and which show no effort. People will meet you half way if you show your efforts and indicate where you are getting stuck.
    – lulu
    Jul 30 at 11:06










  • Okay... Thanks sir
    – Opeyemi Ibrahim
    Jul 30 at 11:31














up vote
-1
down vote

favorite












Question 1:
Last year, a new business purchased 25 tablets, 25 laptops, and 50 desktops, all with three year warranties. The probability a tablet has had warranty work is four times the probability a desktop has had warranty work. The probability a laptop has had warranty work is twice the probability a desktop has had warranty work. Given that 10 computers have used the warranty, (a) If a computer is a laptop, what is the probability it has had warranty work? (b) If a computer has had warranty work, what is the probability it was a laptop? (c) If a computer has had warranty work, what is the probability it was a tablet?



Question 2:
The products of an agricultural firm are delivered by four different transportation companies, A, B, C and D. Company A transports 40% of the products; company B, 30%; company C, 20%; and finally, company D, 10%. During transportation, 5%, 4%, 2%, and 1% of the products spoil with companies A, B, C, and D, respectively. If one product is randomly selected, (a) Obtain the probability that it is spoiled. (b) If the chosen product is spoiled, derived the probability that it has transported by company A.



Question 3:
A salesman in a department store receives household appliances from three suppliers: I, II and III. From previous experience, the salesman knows that 2%, 1%, and 3% of the appliances from suppliers I, II, and III, respectively, are defective. The salesman sells 35% of the appliances from supplier I, 25% from supplier II, and 40% from supplier III. If an appliance randomly selected is defective, find the probability that it comes from supplier III.




probability




share|cite|improve this question

















  • 2




    These are three questions in one post, you better split it up in separate entries. In addition, show some effort of yourself. This site is not meant to provide you an answer just like that.
    – Nicky Hekster
    Jul 30 at 11:02






  • 1




    As you are new to the site: people here tend to not respond well (or at all) to questions like these that look like routine homework problems and which show no effort. People will meet you half way if you show your efforts and indicate where you are getting stuck.
    – lulu
    Jul 30 at 11:06










  • Okay... Thanks sir
    – Opeyemi Ibrahim
    Jul 30 at 11:31












up vote
-1
down vote

favorite









up vote
-1
down vote

favorite











Question 1:
Last year, a new business purchased 25 tablets, 25 laptops, and 50 desktops, all with three year warranties. The probability a tablet has had warranty work is four times the probability a desktop has had warranty work. The probability a laptop has had warranty work is twice the probability a desktop has had warranty work. Given that 10 computers have used the warranty, (a) If a computer is a laptop, what is the probability it has had warranty work? (b) If a computer has had warranty work, what is the probability it was a laptop? (c) If a computer has had warranty work, what is the probability it was a tablet?



Question 2:
The products of an agricultural firm are delivered by four different transportation companies, A, B, C and D. Company A transports 40% of the products; company B, 30%; company C, 20%; and finally, company D, 10%. During transportation, 5%, 4%, 2%, and 1% of the products spoil with companies A, B, C, and D, respectively. If one product is randomly selected, (a) Obtain the probability that it is spoiled. (b) If the chosen product is spoiled, derived the probability that it has transported by company A.



Question 3:
A salesman in a department store receives household appliances from three suppliers: I, II and III. From previous experience, the salesman knows that 2%, 1%, and 3% of the appliances from suppliers I, II, and III, respectively, are defective. The salesman sells 35% of the appliances from supplier I, 25% from supplier II, and 40% from supplier III. If an appliance randomly selected is defective, find the probability that it comes from supplier III.




probability




share|cite|improve this question













Question 1:
Last year, a new business purchased 25 tablets, 25 laptops, and 50 desktops, all with three year warranties. The probability a tablet has had warranty work is four times the probability a desktop has had warranty work. The probability a laptop has had warranty work is twice the probability a desktop has had warranty work. Given that 10 computers have used the warranty, (a) If a computer is a laptop, what is the probability it has had warranty work? (b) If a computer has had warranty work, what is the probability it was a laptop? (c) If a computer has had warranty work, what is the probability it was a tablet?



Question 2:
The products of an agricultural firm are delivered by four different transportation companies, A, B, C and D. Company A transports 40% of the products; company B, 30%; company C, 20%; and finally, company D, 10%. During transportation, 5%, 4%, 2%, and 1% of the products spoil with companies A, B, C, and D, respectively. If one product is randomly selected, (a) Obtain the probability that it is spoiled. (b) If the chosen product is spoiled, derived the probability that it has transported by company A.



Question 3:
A salesman in a department store receives household appliances from three suppliers: I, II and III. From previous experience, the salesman knows that 2%, 1%, and 3% of the appliances from suppliers I, II, and III, respectively, are defective. The salesman sells 35% of the appliances from supplier I, 25% from supplier II, and 40% from supplier III. If an appliance randomly selected is defective, find the probability that it comes from supplier III.





probability





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share|cite|improve this question




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edited Jul 30 at 11:00









Nicky Hekster

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asked Jul 30 at 10:56









Opeyemi Ibrahim

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  • 2




    These are three questions in one post, you better split it up in separate entries. In addition, show some effort of yourself. This site is not meant to provide you an answer just like that.
    – Nicky Hekster
    Jul 30 at 11:02






  • 1




    As you are new to the site: people here tend to not respond well (or at all) to questions like these that look like routine homework problems and which show no effort. People will meet you half way if you show your efforts and indicate where you are getting stuck.
    – lulu
    Jul 30 at 11:06










  • Okay... Thanks sir
    – Opeyemi Ibrahim
    Jul 30 at 11:31












  • 2




    These are three questions in one post, you better split it up in separate entries. In addition, show some effort of yourself. This site is not meant to provide you an answer just like that.
    – Nicky Hekster
    Jul 30 at 11:02






  • 1




    As you are new to the site: people here tend to not respond well (or at all) to questions like these that look like routine homework problems and which show no effort. People will meet you half way if you show your efforts and indicate where you are getting stuck.
    – lulu
    Jul 30 at 11:06










  • Okay... Thanks sir
    – Opeyemi Ibrahim
    Jul 30 at 11:31







2




2




These are three questions in one post, you better split it up in separate entries. In addition, show some effort of yourself. This site is not meant to provide you an answer just like that.
– Nicky Hekster
Jul 30 at 11:02




These are three questions in one post, you better split it up in separate entries. In addition, show some effort of yourself. This site is not meant to provide you an answer just like that.
– Nicky Hekster
Jul 30 at 11:02




1




1




As you are new to the site: people here tend to not respond well (or at all) to questions like these that look like routine homework problems and which show no effort. People will meet you half way if you show your efforts and indicate where you are getting stuck.
– lulu
Jul 30 at 11:06




As you are new to the site: people here tend to not respond well (or at all) to questions like these that look like routine homework problems and which show no effort. People will meet you half way if you show your efforts and indicate where you are getting stuck.
– lulu
Jul 30 at 11:06












Okay... Thanks sir
– Opeyemi Ibrahim
Jul 30 at 11:31




Okay... Thanks sir
– Opeyemi Ibrahim
Jul 30 at 11:31















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