Please answer both questions fully and show work. 2. [Section 2.3] Two engineers
ID: 3298023 • Letter: P
Question
Please answer both questions fully and show work.
2. [Section 2.3] Two engineers, Davis and O'Brien, take turns in measuring hydraulic conductivity (K) of soil samples. Davis succeeds to measure K accurately with probability 1/3 while O'Brien, who is not as careful about following guidance, has 1/4 probability of success. Let us denote A as the event that Davis measures K accurately in one trial, and B for the event that O'Brien measures K accurately in the same trial Assume that we have an infinite set of soil samples with the same correct value, engineer Davis measures K first, and they take turns in taking the measurements. For example, the event that Davis succeeds in taking an accurate measurement in the second trial can be denoted as A B A. If any of the two engineers succeed in getting the accurate value for K they stopped their measuring procedure a. Write down the symbolic expression for event Davis succeeds in the 3'd trial b. What is the probability that Davis succeeds before O'Brien within 3 trials? [8 c. Write down the symbolic expression for event Davis succeeds in the j d. What is the probability that Davis succeeds before O'Brien? [8 pts] using A anmd B [4 pts] ts th trial using A and B, 1 = 1, , j (j > 3). [5 pts] 3. [Section 2.3] Two reinforced concrete buildings A, and B are located in a seismic region. It is estimated that an impending earthquake in the region might be strong (S), moderate (M), or weak (W) with probabilities P(S) = 0.05, P(M) = 0.30, and P(W) = 0.65. The probabilities of failures of A if these earthquakes occur are 0.20, 0.08, and 0.01, respectively occurs. [5 pts] strength? [5 pts] A and B, it is estimated that if building A fails, the probability that building B will also a. Determine the probability of failure of building A if the impending earthquake b. If building A failed, what is the probability that the earthquake was of moderate c. Due to similar procedures used in the design and construction of two buildings,Explanation / Answer
Davis (A)
O'brian(B)
a) A2B2A
B)probability that david wins in 1st trial=2/3 = 0.67
probability that david wins in 2nd trial= 1/3*1/4*2/3=2/36=1/18=0.056
probability that david wins in 3rd trial=1/3*1/4*1/3*1/4*2/3= 2/432 =0.00463
total probability =0.73063
c) A(J-1)B(J-1)A
D)the probability that david succed before o'brian
let david wins in a particular trial both david and o'brian has to fail in all the previous trial
david wins in first trial=2/3
david wins in 2nd trial=2/3(1/3*1/4)
or, 2/3(1/12) =1/18(maximum probability) = 0.056
probability will decrease as the no. of trial increase