# HW #1 - 5. How many 4-letter words can be formed from the...

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1 ISyE 3770 — Fall 2011 Homework #1 (Covers Modules 1.1–1.5) — Due Monday, August 29 1. Suppose we deﬁne the following line segments : U = [0 , 2], A = [0 . 5 , 1], and B = [0 . 5 , 1 . 5]. What are A B , A B , A B , and A B ? 2. Prove DeMorgan’s Laws. You can use Venn diagrams or argue mathematically. 3. A box contains 3 marbles (one red, one green, and one yellow). (a) Consider an experiment that consists of taking one marble from the box, then replacing it in the box, and then drawing a second marble from the box. What is the sample space? (b) Repeat the above when the second marble is drawn without replacing the ﬁrst marble. 4. Let E , F , and G be 3 events. Suppose that U = E F G . Find expressions for the following events: (a) only F occurs. (b) both E and F occur, but not G . (c) at least one event occurs. (d) at least two events occur. (e) all three events occur. (f) none occur. (g) at most one occurs. (h) at most two occur.

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Unformatted text preview: 5. How many 4-letter words can be formed from the alphabet if we require (a) The 2nd letter to be a vowel (a, e, i, o, u)? (b) Exactly one vowel? (c) At least one vowel? 6. As if you have nothing better to do, toss a die 12000 times. (I suppose you can do this in Excel.) How many times do each of the numbers come up? Approximately how many would you expect? 2 7. As if you still have nothing better to do, toss two dice 5000 times. How many times do each of the possible sums come up? Approximately how many would you expect? 8. Toss a coin until you see two Hs in a row. How many tries did it take? Now toss a coin until you see the sequence HT. How long did that take? Thoughts? 9. (Bonus) Three dice are tossed. What is the probability that the same number appears on exactly two of the three dice?...
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## This note was uploaded on 08/27/2011 for the course ISYE 3770 taught by Professor Goldsman during the Spring '07 term at Georgia Institute of Technology.

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HW #1 - 5. How many 4-letter words can be formed from the...

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