A biased coin having probability p of landing heads is tossed repeatedly, with the outcomes of successive tosses being independent. 1. Let X be the number of heads in the first 5 tosses. Find P (X= 2) to three decimal places when p = 14. (a) 0.264; (b) 0.088; (c) 0.313; (d) 0.897; (e) none of these. 2. Let Y be the number of heads in the first 100 tosses. Using an appropriate approximate distribution, find P (Y ≤ 2) to three decimal places when p = 150. (a) 0.639; (b) 0.168; (c) 0.500; (d) 0.677; (e) none of these. 3. Let Z be the number of tails before the first head occurs. Find E[Z] when p = 13. (a) 3; (b) 2; (c) 3 2 ; (d) 1 2; (e) none of these.

A biased coin having probability p of landing heads is tossed repeatedly, with the outcomes of successive tosses being independent. 1. Let X be the number of heads in the first 5 tosses. Find P (X= 2) to three decimal places when p = 14. (a) 0.264; (b) 0.088; (c) 0.313; (d) 0.897; (e) none of these. 2. Let Y be the number of heads in the first 100 tosses. Using an appropriate approximate distribution, find P (Y ≤ 2) to three decimal places when p = 150. (a) 0.639; (b) 0.168; (c) 0.500; (d) 0.677; (e) none of these. 3. Let Z be the number of tails before the first head occurs. Find E[Z] when p = 13. (a) 3; (b) 2; (c) 3 2 ; (d) 1 2; (e) none of these.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 39E: Assume that the probability that an airplane engine will fail during a torture test is 12and that...

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