3) You're tying to plan your school schedule, but there are a bunch of things up in the air. You need to pick one more elective, but you've decided to base your choice based on whether or not your friend tells you if she's taking HISTORY or not. You are trying to decide between MATH, THEATER, or PHILOSOPHY. --There's a 25% chance your friend decides to take HISTORY. If she does, then there's a 40% chance you'll take MATH, 20 % chance you'll take THEATER, and a 40% chance you'll take PHILOSOPHY. --There's a 45% chance your friend decides not take HISTORY. If she tells you she isn't, then there's a 70% chance take THEATER, a 25% chance you take MATH, and a 5% chance you take philosophy. --There's a 30% chance your friend won't let you know in time. If she doesn't tell you, then there's a 50% chance you you'll take MATH and an even split for the other two. Using all of this information, determine the probability that you decide to take MATH. What is the probability that you decide to take THEATER? How about PHILOSOPHY?

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.