8. Capacitors are made by 2 machines, M1 and M2. The probability that a capacitor is manufactured acceptably varies according to the machine. The probabilities are 0.9 and 0.95 respectively for machine M1 and M2. Machine M1 manufactures 80% of the capacitors. (a) Draw a tree diagram and attach the probabilities for every branch and outcome. (b) “Flip the tree” and determine the probability that given it’s an acceptable capacitor it is manufactured by machine M1. (c) Find          (i) P(M1 | not A)          (ii) P(M2 | A)          (iii) P(M2 | not A). You may wish to use Bayes’ Theorem to check your answers.

An engineer decides to buy four new snow tires for his car. He finds that Retailer A is offering a special cash rebate, which depends on how much snow falls during the first winter. If this snowfall is less than 50% of the mean annual snowfall for his city, his rebate will bet 50% of the list price. If the snowfall that winter is more than 50% but less than 75% of the mean annual snowfall, his rebate will be 25% of the list price. If the snowfall is more than 75% of the mean annual snowfall, he will receive no rebate. The engineer finds from a reference book that the annual snowfall for his city has a mean of 80 cm and standard deviation of 20 cm and approximates a normal distribution. The list price for the brand and size of tires he wants is $80.00 per tire. The engineer checks other retailers and finds that Retailer B sells the same brand and size of tires with the same warranty for the same list price but offers a discount of 5% of the list price regardless of snowfall that…

In a large metropolitan city, the probabilities associated with the number of homicides on any given day are as follows: P(0 homicides)=0.40 P(1 homicide) = 0.25 P(2 homicides) = 0.20 P(3 homicides)= 0.15 In On a randomly selected day, what is the probability of at least one homicide? In What is the probability of no homicides on both of 2 randomly selected days? In What is the probability of at least one homicide in 3 randomly selected days?

The probability that Taylor Swift is Austin’s favorite music artist is .10. The probability that he will go to one of her concerts is .84. However, the probability that he does not like Taylor Swift and will go to a concert (because his wife makes him) is .75. a.) Write down the 3 pieces of information given in terms of probabilities involving event A (Taylor Swift is Austin’s favorite music artist) and event B (Austin will go to a Taylor Swift concert).    b.) Summarize the above information using a probability table.   c.) Find the probability that Taylor Swift is Austin’s favorite music artist or Austin will go to a Taylor Swift concert.