MATH 180A – Introduction to Probability Review for Midterm 1 (NOT due) 1. If 8 castles (i.e. rooks) are randomly placed on a chessboard, what are the chances that no rook can capture any of the others? In other words, what is the probability that NO row or column contains two or more rooks? 2. Two dice, one red, the other blue, are rolled. What is the probability that the red die lands on a higher number than the blue die? 3. A woman has n keys that all look alike, of which one will open her door. (a) If she tries the keys at random, discarding those that do not work, what is the probability that she will open the door on her k th try? (b) What if she does not discard previously tried keys? 4. A bleary-eyed student awakens one morning already late for class and randomly pulls two socks out of a drawer containing two black, six brown, and four blue socks. What is the probability that the two socks he draws are a matched pair? 5. Stores A, B and C have 50, 75 and 100 employees and, respectively, 50, 60 and 70
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