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EXAMPLE 2 In trying to figure out the mathematical probability of passing the 5 question T/F quiz, I realized that since each answer has two outcomes, it's kind of like flipping 5 coins when you get heads or tails for each coin. I remembered that you can multiply the outcomes (in this case--two) for each event (answer) to find the total possible ways to answer the quiz. When I mulitplied 2 X 2 X 2 X 2 X 2, which is 2 to the 5th power, not 2 times 5, I got 32. That means there are 32 possible ways to answer the quiz. Only one of those ways would make all 5 answers correct, giving you 100%. Then I had to figure out how many ways you could miss one question and still get a passing grade of 80%. I decided to list the ways in which one answer is wrong and the other four answers are correct: WRRRR RWRRR RRWRR RRRWR RRRRW By adding the 5 possible ways to get an 80% and the 1 way to get 100%, I found the total ways to pass is 6. Therefore, the probability of passing the quiz is only 6/32 or .19 or 19%. |
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