Kindly solve this plz

Problem 1 A preliminary investigation of a site leads an engineer to state that the relative weights are 3 to 5 to 2 (respectively) that the unconfined compressive strength of the soil below is 1200, 1000, or 800 psf (the only three values considered possible, for simplicity). "Undisturbed" samples of the soil will be obtained by boring and tested to gain further information. Owing to the difficulties in obtaining such samples and owing to testing inaccuracies, the following frequencies of indicated strengths are considered applicable for each specimen: P[indicated strength | state ] Indicated strength State 800 1000 1200 800 0.8 0.4 0.2 1000 0.2 0.5 0.3 1200 0,0 0.1 0.5 1.0 1.0 1.0 The engineer calls for a sampling plan of two independent specimens. (a) Find the conditional probabilities of each of the possible outcomes of this sample of size two given that the true strength is 1200 psf. (b) If the results of the sampling were one specimen indicating 1000 and one indicating 800 psf, find the engineer's posterior probabilities of the strength. (c) Suppose that after these two specimens the engineer continued sampling and found an uninterrupted sequence of specimens indicating 1200 psf. After how many could he stop: (i) Confident that the strength was not actually 800? (ii) At least "90 percent confident" that the strength was actually 12007 Note: In your solutions, please use the following notation: T - (True strength is i) ; Z = (strength indicated by specimen j is i)