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homework02 - c(2 pts In the Powerball lottery game the...

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Probability for Engineering Applications Assignment #2, due at the beginning of class on Thursday, February 2 nd , 2006 1. (1 pt) (Textbook exercise 2.19) Show that the probability that exactly one of the events A or B occurs is given by P [ A ] + P [ B ] - 2 P [ A B ]. 2. (1 pt) (Textbook exercise 2.20) Let the events A and B have P [ A ] = x , P [ B ] = y and P [ A B ] = z . Use Venn diagrams to find P [ A C B C ], P [ A B C ], P [ A C B ] and P [ A C B C ]. 3. (1 pt) (Textbook exercise 2.29) The lifetime of a device behaves according to the expo- nential probability law introduced in Example 2.10 ( P [( t, )] = e - αt for t > 0), with α = 1. Let A be the event “lifetime is greater than 5” and B the event “lifetime is greater than 10”. a. Find the probability of A B and A B . b. Find the probability of the event “lifetime is greater than 5 but less than or equal to 10”. 4. (5 pts) Find the following: a. (1 pt) The campus computer store sells computer hard disks from 4 different manufac- turers. In how many ways can you buy 6 disks from the computer store? b. (1 pt) If a polygon has 42 sides, how many diagonals does it have?
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Unformatted text preview: c. (2 pts) In the Powerball lottery game, the object of the game is to choose 5 numbers from 1 to 49, and then the additional “Powerball” number from 1 to 42. After a number is drawn to become one of the 5 from 1 to 49, it cannot be drawn again. However, any number from 1 to 42 can be drawn as the “Powerball”. Also, the order of the numbers does not matter. What is the probability of winning the Powerball lottery? d. (1 pt) How many possible batting orders (i.e. the sequence in which players come in to bat) are there for a team of nine players? 5. (2 pts) A box contains N marbles. Of these, M are taken out at random, marked and returned to the box. The contents of the box are then thoroughly mixed. Next, n marbles are drawn at random from the box and the marked marbles are counted. What is the probability that x of these n marbles are marked? 1...
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