100 integrated circuits of type A, 200 of type B, and 300 of type C are mixed together. Type A chips are known to be defective with probability 1/10, type B with probability 1/20, and type C with probability 1/30. a) If all 600 chips are mixed together and one is selected at random, what is the probability of its being defective? b) Given that the selected chip in part (a) is defective, what is the probability that it is type A?
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- ) Mars, Inc. states that 24% of its M&M plain candies are blue and that 16% are green. Assume that they are correct and a large random sample of plain M&Ms is randomly selected from the factory.a.) What is the probability that three candies selected from the sample will be either both greenor both blue?b.) What is the probability that if four candies were selected from the sample that at least onewould be not green and not blue?c.) What is the probability that if twenty M&Ms were eaten randomly from the sample, thatexactly six of them would be green? d.) Find the mean and standard deviation for the above binomial probability distribution inpart c. Based on that, would it be unusual that exactly six would be green from a randomselection of twenty M&Ms? Why or why not?8) In a class of 100 half the students are science majors and half are liberal art majors. A student who is a science major has a 0.9 probability of passing a given test whilst a student who is liberal art major has only a probability of 0.7. We pick 2 students at random without replacement and give them the test. What is the probability that both students pass the exam?1) A particular gadget contains 50 integrated circuits (ICs). The probability that any one of these ICs is defective is 0.02. The gadget will function only if there is no defective IC. What is the probability that the gadget will function?
- The large bag of chocolates contains: 38 milk chocolates (MC), 31 Mr. Goodbars (G), 33, Krackels (K), and 33 Special Darks (S). We are going to randomly select one candy and put it back (replace it); then, we are going to select a second candy. What is the probability that the first chocolate is a Krackel and the second is a Special Dark?The large bag of chocolates contains: 38 milk chocolates (MC), 31 Mr. Goodbars (G), 33, Krackels (K), and 33 Special Darks (S). We are going to randomly select one eat it (not replace it); then, we are going to select a second candy. What is the probability that the first chocolate is a Krackel and the second is a Special Dark?The distribution of car rental by municipal members from the three companies is as follows:60% from company1, 30%from company2 and 10% from company3. According to historical data, 9% of vehicles from company1, 20% of vehiclesfrom company2 and 6% of vehicles from company3 require maintenance,a) What is the probability that a vehicle rented to the municipality will require maintenance?b) What is the probability that the vehicle that needs maintenance is from the 2nd company?
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- a) A certain company sends 40% of its overnight mail parcels via express mail service E₁. Of these parcels, 2% arrive after the guaranteed delivery time( L - the event late delivery). If a record of overnight mailing is randomly selected from the company's file, what is the probability that the parcel went via E, and was late? Suppose that 50% of the overnight parcels are sent via express mail E, and the remaining 10% are sent via E3 Of those sent via E₂, only 1% arrive late, whereas 5% of the parcels handled by E, arrive late. b) What is the probability that a randomly selected parcel arrived late? c) If a randomly selected parcel has arrived on time, what is the probability that it was not sent via E₁.Sadie inspects a batch of products by sampling 4 of them without replacement. If at least one of the products is defective in the sample, the whole batch is sent back.Sadie doesn't know it, but in the batch she is inspecting now, there are 100 products and 11 are defective. If she samples 4 products from this batch without replacement,what is the probability that... a) All of the products in the sample will be defective? b) None of the products in the sample are defective? c) At least one of the products is defective and the whole batch is sent back? For all of the above, round to four decimal places.How would I approach this problem?