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.
A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc42a076-5c06-46af-a63c-d94f125ca0b9%2F755e28c8-8fa6-4912-a2ad-9f045e2dda1d%2Fh62p6r4_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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.
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