18. sherlock Holmes has rounded up all 7 suspects in the case of the theft of th

Question

18. sherlock Holmes has rounded up all 7 suspects in the case of the theft of the rubber ducky. For 4 of the suspects, Holmes has assigned probabilities to each suspect, that they committed the theft. Refer to the suspects as A, B, C, D, E, F, G. Holmes figures the probability as .1 for A, .05 for B,.05 for C, and .2 for D. He doesn't know the probabilities for E, F, and G, but he figures both suspects E and F are twice as likely to have done it as suspect G. He also figures suspects E and F are equally likely to have done it. Calculate the probabilities for suspects E, F, and G. (Show your work) Holmes is determined to recover this priceless artifact, and decides there is a reasonable chance that the thief has the rubber ducky on his person. He decides that suspects A, B, C, and D are equally likely to have the item, and that probability is 75 percent. Suspects E, F, and G are equally likely to have the item, and that probability is 80 percent. Find that the rubber ducky is in the room. (Show your work)

Explanation / Answer

Answer:

Part I:

Total number of suspects = 7

Also, based on given conditions:

Therefore P(E) = 0.24, P(F) = 0.24 and P(G) = 0.12

Total Probability = (0.1 + 0.05 + 0.05 + 0.2+0.24+0.24+0.12) = 1

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