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HW2soln

# HW2soln - Homework 2 Due on Friday am For each problem just...

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Homework 2 Due on Friday, May 30, 11am. For each problem just giving the answer will not suffice; a proper argument is required. Problem 1 A lock on a lab door has buttons numbered 0 through 9. The right code for opening the lock is 8542. Also, if on three consecutive attempts, a wrong code (a code is a combination of 4 ordered distinct digits) is entered, then a burglar alarm is let off. Anna forgot the right code, but remembers that the code consists of 4 distinct digits. So she keeps on trying one code after another without replacement. Compute the probability that she gets in (without letting off the alarm). Please report the answer in p q form, it’s OK to not simplify. Solution Total number of codes ( ie , ordered combination of 4 distinct digits) = 10 · 9 · 8 · 7 = 5040 No. of ways in which Anna will NOT get the correct code in the three trials = 5039 · 5038 · 5037 Thus, probability of Anna’s getting in = 1 - 5039 · 5038 · 5037 5040 · 5039 · 5038 = 1 - 5037 5040 = 3 5040 = 1 1680 Problem 2 An urn contains 10 Red and 5 black balls. Two balls are picked (one after the other) from the urn.

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HW2soln - Homework 2 Due on Friday am For each problem just...

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