Lee forgot to study for her geography quiz, but she was not too worried because the quiz had only five true-false questions.Suppose she guessed all of the answers.What are the chances that she passed with four or five correct answers?
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To calculate the chances that Lee passed with four or five correct answers, we need to determine the probability of getting each possible number of correct answers.
Let's start by calculating the probability of getting one correct answer. Since the quiz has only two possible answers (true or false) and Lee is blindly guessing, the probability of getting one correct answer is 1/2.
Now, let's calculate the probability of getting four correct answers. Since Lee is guessing for each question, there are two possibilities: she guesses all four correctly, or she guesses three correctly and one incorrectly. The probability of guessing one question correctly is still 1/2. Thus, the probability of guessing four correct answers is:
(1/2) * (1/2) * (1/2) * (1/2) = 1/16
Finally, let's calculate the probability of getting five correct answers. Similarly, there are two possibilities: she guesses all five correctly, or she guesses four correctly and one incorrectly. The probability of guessing one question correctly remains 1/2. Therefore, the probability of guessing five correct answers is:
(1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/32
To find the overall probability of passing with four or five correct answers, we add the probabilities calculated for each case:
1/16 + 1/32 = 3/32
Therefore, the chances that Lee passed with four or five correct answers are 3/32.