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Each day, Antonio eats a big breakfast with probability 0.4, a small breakfast with probability 0.2,...

Each day, Antonio eats a big breakfast with probability 0.4, a small breakfast with probability 0.2, and otherwise skips breakfast. On days where he eats a big breakfast, he eats a big lunch with probability 0.2, a small lunch with probability 0.7, and otherwise he skips lunch. On days where he eats a small breakfast, he eats a big lunch with probability 0.1, a small lunch with probability 0.6, and otherwise he skips lunch. On days when he skips breakfast, Antonio eats a big lunch with the probability 0.8 and otherwise he eats a small lunch. (Antonio never skips lunch on a day when he skips breakfast.) On a randomly selected day, what is the probability that Antonio eats a big lunch? On a randomly selected day, if Antonio skips lunch, what is the probability he ate a small breakfast?

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