a) A fair coin is tossed 4 times. ¡) Use counting methods to find the probability of getting 4 consecutive heads HHHH. ii) Use counting methods to find the probability of getting the exact sequence HTHT. iii) Common sense and experience in coin-tossing might suggest that obtaining a pattern of 4 consecutive heads in (i) is far less likely than obtaining the pattern we see in (ii). Is this a flawed viewpoint? Give a clear decisive answer. Vague answers will not receive marks.
a) A fair coin is tossed 4 times. ¡) Use counting methods to find the probability of getting 4 consecutive heads HHHH. ii) Use counting methods to find the probability of getting the exact sequence HTHT. iii) Common sense and experience in coin-tossing might suggest that obtaining a pattern of 4 consecutive heads in (i) is far less likely than obtaining the pattern we see in (ii). Is this a flawed viewpoint? Give a clear decisive answer. Vague answers will not receive marks.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![a) A fair coin is tossed 4 times.
¡) Use counting methods to find the probability of getting 4 consecutive heads HHHH.
ii) Use counting methods to find the probability of getting the exact sequence HTHT.
iii) Common sense and experience in coin-tossing might suggest that obtaining a pattern of 4 consecutive heads in (i) is far less likely than
obtaining the pattern we see in (ii). Is this a flawed viewpoint? Give a clear decisive answer. Vague answers will not receive marks.
iv) With respect to this question, why is it far more likely to get a pattern (with 2 heads) as in part (ii) than a string with 4 heads as in part (i)?
Do a formal calculation of probabilities [P(H = 2) and P(H = 4)] to back up your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1e1e8b5a-27be-4811-81c5-ae79726012ba%2F51adc656-def1-4f41-906a-7642e7ee90cd%2Fqxj4cd8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:a) A fair coin is tossed 4 times.
¡) Use counting methods to find the probability of getting 4 consecutive heads HHHH.
ii) Use counting methods to find the probability of getting the exact sequence HTHT.
iii) Common sense and experience in coin-tossing might suggest that obtaining a pattern of 4 consecutive heads in (i) is far less likely than
obtaining the pattern we see in (ii). Is this a flawed viewpoint? Give a clear decisive answer. Vague answers will not receive marks.
iv) With respect to this question, why is it far more likely to get a pattern (with 2 heads) as in part (ii) than a string with 4 heads as in part (i)?
Do a formal calculation of probabilities [P(H = 2) and P(H = 4)] to back up your answer.
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