TP%234_f08 - )) ( ) 2 ( ) 1 (( n foot in rock no foot in...

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CE3120 Spring 2008 Thought Problem 4 Pile Driving When driving piles for footings or foundations you want the piles to extend from the surface down to bedrock. Sometimes, however, a pile will strike rock through which it cannot be driven. Such interrupted piles can not be relied on to carry the same load as a pile driven all the way to bedrock. Find the probability that a pile will reach bedrock n feet fellow the surface without hitting a rock. The probability is p that the pile will strike rock in any foot, and the occurrence of rocks in different (non-overlapping) 1-foot intervals are independent random events. Compute the probability of making it to 10 feet and 20 feet, when p=1/20. How about 10 feet and 20 feet when p=1/10?
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CE 3102 Spring 2008 Thought Problem 4 Instructor’s Partial Solution The probability of reaching bedrock can be written as
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Unformatted text preview: )) ( ) 2 ( ) 1 (( n foot in rock no foot in rock no foot in rock no P K Since striking a rock in each foot can be treated as independent events, this probability can be rewritten as the product of the individual event probabilities ) ( ) 2 ( ) 1 ( n foot in rock no P foot in rock no P foot in rock no P K The probability of striking a rock for each foot is p, so the probability of not striking a rock in (1-p) for each foot. The probability of making it to n feet is then n p bedrock reaching P ) 1 ( ) ( = For p=1/20 and n=10 feet, 5987 . ) 05 . 1 ( ) ( 10 = bedrock reaching P For p=1/20 and n=20 feet, 3585 . ) 05 . 1 ( ) ( 20 = bedrock reaching P For p=1/10 and n=10 feet, 3487 . ) 1 . 1 ( ) ( 10 = bedrock reaching P For p=1/10 and n=20 feet, 1216 . ) 1 . 1 ( ) ( 20 = bedrock reaching P...
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TP%234_f08 - )) ( ) 2 ( ) 1 (( n foot in rock no foot in...

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