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MA22S6 Numerical and Data Analysis Homework sheet 2 1 2015-2016 Due Thursday, 11 February 2016 in class Justify your answers by a few words, in particular when using a formula. 1. What is the probability of drawing 4 aces if we draw 4 cards out of a 52-card deck without replacement? 2. What is the largest number you can reach if you count in binary on your fingers (using two hands and staring from 1)? 3. Five married couples have bought 10 seats in a row for a concert. In how many different ways can they be seated a) with no restriction ? b) if each couple is to sit together? c) if men and women sit separately ? 4. Suppose you’re on a game show, and you’re given the choice of four doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the other doors, opens another door, say No. 2, which has a goat. He then says to you, ’Do you want to change your mind and pick one of doors No. 3 or 4?’ Is it to your advantage to do the switch? What is the probability to win for either strategy? 5. In testing a certain kind of truck tire over a rugged terrain, it is found that 25% of the trucks fail to complete the test run without a blowout. Of the next 15 trucks tested, find the probability that a) 3 have a blowout b) from 3 to 6 have blowouts c) fewer than 4 have blowouts 1 Lecturer: Stefan Sint, sint@maths.tcd.ie, see also http://www.maths.tcd.ie/~sint/MA22S6/MA22S6.html 1