Question 1: Permutations and combinations (30 points) Suppose that there are 31 drone delivery companies in a given city
Posted: Wed Jul 06, 2022 12:21 pm
Question 1: Permutations and combinations (30 points)
Suppose that thereare 31 drone delivery companies in a given city, out of which 10are small companies and 15 are big companies. Suppose that in total6 drone delivery companies are randomly selected. Suppose also thatevery outcome is equally likely.
a) Find thenumber of all possible outcomes in the sample space for this randomexperiment. [10 points]
b) Find the number ofall possible outcomes for the event when there will be exactly 5small companies if you randomly select 6 out of the 31 dronedelivery companies? [10 points]
c) What is theprobability that there will be exactly 5 small companies if yourandomly select 6 out of the 31 drone delivery companies? [10points]
Question 2: Conditional probability, Bayes' theorem (30points)
Consider anelectronics repair shop with 4 different services. Suppose that 70%of the devices will need service 1, 10% of the devices will needservice 3, and 5% of the devices will need service 4. Of thedevices that will need service 1, 10% will have an extra charge, ofthe c devices that will need service 2, 1.5% will have an extracharge, of the devices that will need service 3, 99% will not havean extra charge, and of the devices that will need service 4, 98%will not have an extra charge.
a) Find theprobability that the devices will need service 2, and draw thecomplete tree diagram. [10 points]
b) What is theprobability that a randomly selected device will have an extracharge? [10 points]
c) If we know that arandomly selected device will have an extra charge, what is theprobability that the devices will need service 3? [10 points]
i'llappreciate if you solved them all, i'll give thumps up forsure
i hope thatdifferent expert can help me
Suppose that thereare 31 drone delivery companies in a given city, out of which 10are small companies and 15 are big companies. Suppose that in total6 drone delivery companies are randomly selected. Suppose also thatevery outcome is equally likely.
a) Find thenumber of all possible outcomes in the sample space for this randomexperiment. [10 points]
b) Find the number ofall possible outcomes for the event when there will be exactly 5small companies if you randomly select 6 out of the 31 dronedelivery companies? [10 points]
c) What is theprobability that there will be exactly 5 small companies if yourandomly select 6 out of the 31 drone delivery companies? [10points]
Question 2: Conditional probability, Bayes' theorem (30points)
Consider anelectronics repair shop with 4 different services. Suppose that 70%of the devices will need service 1, 10% of the devices will needservice 3, and 5% of the devices will need service 4. Of thedevices that will need service 1, 10% will have an extra charge, ofthe c devices that will need service 2, 1.5% will have an extracharge, of the devices that will need service 3, 99% will not havean extra charge, and of the devices that will need service 4, 98%will not have an extra charge.
a) Find theprobability that the devices will need service 2, and draw thecomplete tree diagram. [10 points]
b) What is theprobability that a randomly selected device will have an extracharge? [10 points]
c) If we know that arandomly selected device will have an extra charge, what is theprobability that the devices will need service 3? [10 points]
i'llappreciate if you solved them all, i'll give thumps up forsure
i hope thatdifferent expert can help me