Question

An exam consists of 15 multiple-choice questions. Each of the 15 answers is either right or wrong Suppose the probability that a student makes lewer than 3 mistakes on the exam is 0.43 and that the probability that a student makes from 3 to 11 (inclusive) mistakes is 0.27 Find the pibbability of each of the following outcomes

a. A student makes more than 11 mistakes
b. A student makes 3 or more mistakes
c. A student makes at most 11 mistakes
d. Which two of these three events are complementary?

Answer 1

To find the probability of each outcome, we need to first determine the probabilities of the complementary events.

Step-by-step explanation:

To find the probability of each outcome, we need to first determine the probabilities of the complementary events.

a. A student makes more than 11 mistakes:

This is the complement of the event of making 11 or fewer mistakes. So, the probability of making more than 11 mistakes is 1 minus the probability of making at most 11 mistakes.

To find the probability of making at most 11 mistakes, we subtract the probability of making 3 to 11 mistakes (inclusive) from the total probability of making fewer than 3 mistakes.

b. A student makes 3 or more mistakes:

This event can be found by subtracting the probability of making fewer than 3 mistakes from the complement of making at most 11 mistakes.

c. A student makes at most 11 mistakes:

To find the probability of this event, we just need to subtract the probability of making more than 11 mistakes from 1.

d. Which two of these three events are complementary:

The complements of events a and c are complementary because they represent opposite outcomes.