How many casts are there which include at most one of

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to be leads togehter. How many casts are there which include at most one of Quinn and Jordan as a lead? (Again, only this condition, not the previous two.) 3 3.1 We have five bags. Each bag has five balls; in the first bag, 1 is red and 4 are blue, in the second 2 are red and 3 are blue, and so on. We randomly (with equal likelihood) choose a bag and then randomly choose a ball. How likely is it that we get a red ball? 1
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3.2 Call A the event that we reach into the fourth bag (the one with 4 red and 1 blue). Call B the event that we get a red ball. What is P ( A | B )? (In other words, after we see that we got a red ball, how likely is it that we got it from the fourth bag.) 4 4.1 The fire alarms are very sensitive, and will detect a fire with 99 . 9% certainty. Unfortunately, because they are so sensitive, they also go off 1% of days when there isn’t a fire. A fire actually has a 1 / 500 change of happening on a given day. Each day, what is the likelihood of the fire alarm going off? 4.2 When the fire alarm does go off, what is the likelihood that there really is a fire? 4.3 It rains on 10% of days, and whether there’s a fire is independent of whether it rains. What is the chance on a given day that it will rain and there will be a fire? 5 5.1 We flip a fair coin three times, and get paid the square of the number of tails in dollars. Call the amount we get paid X . What is E ( X )? 5.2 What is var ( X )? 5.3 What is sd ( X )? 2
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