Final answer:
To determine the probability of Edith passing a multiple choice test by randomly guessing, we need to calculate the chances of her getting at least 4 out of 5 questions correct, assuming each question has 5 answer options. This situation can be modeled as a binomial probability problem, with the total passing probability being the sum of the individual probabilities of getting exactly 4 and exactly 5 correct answers.
Step-by-step explanation:
To find the probability that Edith passes a multiple choice test with 5 questions by guessing randomly, we must consider that she needs to get 70% or more of the questions correct to pass. Given that each question has 5 options, the probability of guessing a single question correctly is 1/5 or 0.2.
Since Edith needs a score of 70% or more for a test with 5 questions, she would have to get at least 4 questions right. The number of correct answers Edith can get is therefore either 4 or 5. This is a binomial probability problem because there are two outcomes for each question (correct or incorrect), a fixed number of trials (5 questions), and the probability of success (guessing correctly) is consistent across trials (0.2).
To calculate the combined probability of getting exactly 4 and exactly 5 correct answers, we add the probabilities of each of these two outcomes. Using the binomial probability formula:
- Probability of getting exactly 4 correct answers: P(X=4) = (5 choose 4) × (0.2)^4 × (0.8)^1.
- Probability of getting all 5 correct answers: P(X=5) = (5 choose 5) × (0.2)^5 × (0.8)^0.
We calculate these probabilities and add them together to find the total probability of passing the test by guessing.
Please note that the calculations will require a binomial probability formula or a probability distribution function calculator to compute the exact values. The key concept is understanding how the binomial distribution works and how it is applied in this scenario.