Each night, a princess is equally likely to sleep on anything from 6 to 12 mattresses. On half of the nights of the year, a pea is placed underneath the lowest mattress. If the pea is placed underneath 6 mattresses, she sleeps well 0 nights out of 10. She never sleeps! If the pea is placed underneath 7 mattresses, she sleeps well 1 night out of 10. If the pea is placed underneath 8 mattresses, she sleeps well 2 nights out of 10. If the pea is placed underneath 9 mattresses, she sleeps well 3 nights out of 10. If the pea is placed underneath 10 mattresses, she sleeps well 4 nights out of 10. If the pea is placed underneath 11 mattresses, she sleeps well 5 nights out of 10. If the pea is placed underneath 12 mattresses, she sleeps well 6 nights out of 10. One morning, when her good friend Mr Bayes woke her up, she said that she had slept incredibly well that night! What is the expected number of mattresses that she slept on that night?
Each night, a princess is equally likely to sleep on anything from 6 to 12 mattresses. On half of the nights of the year, a pea is placed underneath the lowest mattress. If the pea is placed underneath 6 mattresses, she sleeps well 0 nights out of 10. She never sleeps! If the pea is placed underneath 7 mattresses, she sleeps well 1 night out of 10. If the pea is placed underneath 8 mattresses, she sleeps well 2 nights out of 10. If the pea is placed underneath 9 mattresses, she sleeps well 3 nights out of 10. If the pea is placed underneath 10 mattresses, she sleeps well 4 nights out of 10. If the pea is placed underneath 11 mattresses, she sleeps well 5 nights out of 10. If the pea is placed underneath 12 mattresses, she sleeps well 6 nights out of 10. One morning, when her good friend Mr Bayes woke her up, she said that she had slept incredibly well that night! What is the expected number of mattresses that she slept on that night?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Each night, a princess is equally likely to sleep on anything from 6 to 12 mattresses. On half of the nights of the year, a pea is placed underneath the lowest mattress.
If the pea is placed underneath 6 mattresses, she sleeps well 0 nights out of 10. She never sleeps!
If the pea is placed underneath 7 mattresses, she sleeps well 1 night out of 10.
If the pea is placed underneath 8 mattresses, she sleeps well 2 nights out of 10.
If the pea is placed underneath 9 mattresses, she sleeps well 3 nights out of 10.
If the pea is placed underneath 10 mattresses, she sleeps well 4 nights out of 10.
If the pea is placed underneath 11 mattresses, she sleeps well 5 nights out of 10.
If the pea is placed underneath 12 mattresses, she sleeps well 6 nights out of 10.
One morning, when her good friend Mr Bayes woke her up, she said that she had slept incredibly well that night!
What is the expected number of mattresses that she slept on that night?
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