Question

4-2. Piles are used to support the foundation of a structure. The failure probability of a pile during proof testing is 0.1. Determine the following: (a) The probability of three failed piles out of ten tested piles (b) The probability of no failures in 20 tested piles (c) The probability of ten tested piles to obtain the first failure (d) The probability of three consecutive pile failures dan w ahilitu af 002 The 11

Answer 1

a)

here this is binomial with parameter n=10 and p=0.1

probability =

P(X=3)=

(nCx)px(1−p)(n-x)    =

0.0574

b)

P(no failures in 20 ) =(1-0.1)²⁰ =0.1216

c)

P(ten tested pile to get first failure) =P(first 9 not failed and 10 th failed) =(1-0.1)⁹*0.1 =0.0387

d)

P(3 consecutive pile failure) =0.1*0.1*0.1 =0.001