What is the smallest in m such that p(someone in the group shares your birthday)

Question

What is the smallest in m such that p(someone in the group shares your birthday)>.5? Before a factory can ship a part, it is inspected twice. There are 7 machines available for testing and each part can be tested on any 2 of the machines. How many ways are there to select the 2 machines that the part will be tested on? (15 points ) A warehouse uses 3 different shipping methods: UPS, FedEx. and USPS. For each service, the percentages of packages that are regular delivery and express delivery The event R refers to package being shipped via regular delivery and R refers to a package that is shipped via express delivery. The events D1,D2,and D3 represent a package coming from UPS, FedEx, and USPS, respectively. What is the probability that a randomly selected order is shipped via UPS? What is the probability that a randomly selected order is shipped via express delivery? What is the probability that a randomly selected order is shipped via USPS or regular delivery? what is the probability that a randomly selected order is shipped via FedEx and express delivery? All parts coming off a production line are scanned by a laser to measure their length and determine if they meet manufacturing specifications. Based on historical studies of the process, it is believed that 2.2% of the parts are actually defective. The event D refers to an item actually being defective and D refers to an item that is not defective. The event F refers to an item that fails the scanning inspection and is labelled as defective and F refers to an item that passes the test. Given that a randomly selected part has failed the scanning, what is the probability the part actually is defective? Hint, use Baye's theorm!

Explanation / Answer

The probability that randomly selected order shipped via UPS =48% =0.48

b)The probability that randomly selected order shipped via express delivery =40% =0.40

c) The probability that randomly selected order shipped via USPS or regular delivery=25%+60%-15%=70%=0.7

d) The probability that randomly selected order shipped via Fedex and express delivery=19%=0.19

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