Final answer:
To calculate the probability that Kyle does not pass and Arlo does pass a true-false 10-question quiz, we use the binomial probability formula, considering passing as getting at least 70% correct. We add the probabilities for Kyle to get 0 to 6 correct answers and for Arlo to get at least 7 correct answers, then multiply the two probabilities for the final answer.
Step-by-step explanation:
To find the probability that Kyle does not pass and Arlo does pass, we need to consider separate probabilities of each event and assume that these events are independent.
Let's assume 'passing' the quiz means scoring at least 70%. For a true-false quiz with 10 questions, each question has a probability of ½ of being correct if the student guesses.
For Kyle to not pass, he must get less than 70% of the questions correct, which means 6 or fewer correct answers.
For Arlo to pass, he needs at least 7 correct answers. We will calculate these probabilities using the binomial probability formula:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
where:
- C(n, k) is the number of combinations of n items taken k at a time
- p is the probability of success on an individual attempt
- n is the number of independent trials
- k is the number of successes
Therefore, we first find the probability of Kyle not passing by adding the probabilities of him getting 0 to 6 questions right.
Then we calculate the probability of Arlo passing by finding the probability of him getting at least 7 questions right.
Lastly, since the events are independent, we multiply the two probabilities together to get the final answer.
Since an explicit numeric answer has not been given, further calculations are necessary to provide a precise value.