Given that a person is innocent, suppose that the probability of his or her DNA matching that found at the crime scene is only 0.000001, one in a million. Further, given that a person is guilty, suppose that the probability of his or her DNA matching that found at the crime scene is 0.99. Jane Doe's DNA matches that found at the crime scene. Complete parts a through a below. a. Find the probability that Jane Doe is actually innocent, if absolutely her probability of innocence is 0.57. Interpret this probability. Show your solution by introducing notation for events, specifying probabilities that are given, and using a tree diagram to find your answer. Match (0.000001) Innocent (0.5) No Match() Match (0.99) Guilty (0.5) No Match ( (Type integers or decimals. Do not round.) The probability is $P(\text{match } | \text{ innocent})=0.000001$ (Round to eight decimal places as needed) b. Repeat part a if the unconditional probability of innocence is 0.96. Compare results. The probability becomes 0.0001 (Round to eight decimal places as needed.) c. Explain why it is very important for a defense lawyer to explain the difference between $P(\text{match } | \text{ innocent})$ and $P(\text{innocent } | \text{ match})$. When the absolute probability of innocence is large and $P(\text{match } | \text{ innocent})$ is small, the probability $P(\text{innocent } | \text{ match})$ can be significantly larger than $P(\text{match } | \text{ innocent})$. Enter your answer in each of the answer boxes.
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