a multiple choice test consists of 8 questions, each with 4 possible answers but only one of which is correct.what is the probability that an unprepared student will, by chance, get,
a. all correct answers,
b. exactly 5 correct answers,
c. at most 4 correct answers,
d. at most 6 incorrect answers
please tell me answer for this question I have a tomorrow
To calculate the probabilities, we need to know the total number of possible outcomes and the favorable outcomes. In this case:
Total number of possible outcomes = 4^8 (since each question has 4 possible answers)
a. To find the probability of getting all correct answers, we need to find the number of favorable outcomes, which is 1 (since there is only one combination of all correct answers). Therefore, the probability is 1/4^8.
b. To find the probability of exactly 5 correct answers, we need to calculate the number of favorable outcomes. There are different ways to get 5 correct answers out of 8 questions, so we need to calculate the combinations. This can be calculated using the binomial coefficient formula. The number of favorable outcomes for exactly 5 correct answers is (8 choose 5) = 8! / (5! * (8-5)!). Therefore, the probability is (8! / (5! * (8-5)!)) / 4^8.
c. To find the probability of at most 4 correct answers, we need to calculate the number of favorable outcomes for 0, 1, 2, 3, or 4 correct answers, and add them up. We can calculate each individually using the method mentioned in part b. Then, we divide the sum by 4^8 to get the probability.
d. To find the probability of at most 6 incorrect answers, we calculate the number of favorable outcomes for 0, 1, 2, 3, 4, 5, or 6 incorrect answers. Similar to part c, we calculate each individually and then divide the sum by 4^8 to get the probability.