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  3. 3 when it is raining on a saturday the probability...

Question: 3 when it is raining on a saturday the probability...

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3. 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 mathematically 4. Suppose that one die is rolled and you observe the number of dots facing up. The sample space for this experiment is S -(1, 2, 3, 4, 5, 6). The following table provides 5 different potential probability assignments to the possible outcomes Outcome Assignment AssignmentAssignment Assignment Assignment #1 0 16 #2 #3 #4 #5 0.13 0.3 0.1 0.08 0.21 0.18 16 4 4 16 4 0.5 0.5 16 6 a) which of the assignments #1-#5 are legitimate probability assignments? Explain your answers b) Let A die comes up even; B die comes up at least 2; C-die comes up at most 5; D die comes up 1. c) Determine the probability that you observe a die roll which is a multiple of 3. Use each of the legitimate Determine the probability of each of these four events using each of the legitimate probability assignments probability assignments Determine the probability that you observe a prime number on a die roll (note: one is not a prime number). Use each of the legitimate probability assignments If the die is balanced (i.e. fair), which probability assignment would be appropriate? Why? using probability assignment #5 and the events defined in part b) above, find PA n B), P(B n C), P(B U C), P(An D), P(A U C), P(DIB), and P(A U (B n c)) d) e) f)

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