Probability

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1. The probability of passing a 30 question multiple choice test by randomly guessing the answers is 0.25. What is the probability of failing the test if guessing randomly? Answer as a decimal number with 4 digits of precision.

2. The probability of Mary wearing blue tomorrow is 0.54. The probability of John wearing blue tomorrow is 0.29. The probability of BOTH Mary and John wearing blue tomorrow is 0.05. What is the probability that at least one of Mary or John is wearing blue tomorrow?

3. My Uncle Ryan has a weighted coin, that comes up heads more often than a "fair" coin. The probability of his coin coming up heads is 0.88. If I flip his coin 6 times in a row, what is the probability that all 6 flips are heads up? Give your answer in decimal form, with 4 digits of precision.

4. The probability of me catching the bus on time is 0.32. The probability of getting to work on time, given that I caught the bus on time, is 0.88. What is the probability that I caught the bus on time AND got to work on time? Give your answer as a decimal value and with 4 digits of precision.