Final answer:
To find the probability of each outcome, we need to consider the given probabilities and apply probability rules. The probability of each outcome is as follows: a. A student makes more than 1 mistake: 0.73 b. A student makes 8 or more mistakes: 0.57 c. A student makes at most 19 mistakes: 0.73 d. The two complementary events are making more than 1 mistake and making at most 19 mistakes.
Step-by-step explanation:
To find the probability that a student makes more than 1 mistake, we can subtract the probability of making 1 or fewer mistakes from 1. The probability of making fewer than 8 mistakes is given as 0.27, so the probability of making 1 or fewer mistakes is 0.27. Therefore, the probability of making more than 1 mistake is 1 - 0.27 = 0.73.
To find the probability that a student makes 8 or more mistakes, we can subtract the probability of making fewer than 8 mistakes from 1. The probability of making from 8 to 15 mistakes is given as 0.43. Therefore, the probability of making 8 or more mistakes is 1 - 0.43 = 0.57.
To find the probability that a student makes at most 19 mistakes, we can subtract the probability of making 20 or more mistakes from 1. Since the total number of questions is 50, the probability of making 20 or more mistakes is the complement of the probability of making fewer than 20 mistakes. Therefore, the probability of making at most 19 mistakes is 1 - 0.27 = 0.73.
The two events that are complementary are making more than 1 mistake and making at most 19 mistakes, since they cover all possible outcomes.