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When it is raining on a Saturday, the probability Tyler stays at home to play video games is 0.80, otherwise, he will go outside with friends. When it is not raining, the probability that Tyler goes out with friends is 0.70. According to the weather forecast, the probability of raining this Saturday is 0.60 a) What is the probability that it is raining and Tyler is home playing video games on Saturday? b) What is the probability that it is raining and Tyler goes outside with his friends on Saturday? c) What is the probability that Tyler goes outside with his friends on Saturday? d) If Tyler stays home to play video games, what is the probability it is not raining on Saturday? e) Is Tyler going outside with friends independent of whether it is raining or not? Support your answer 3. mathematically

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