A student studies for a statistics exam where all questions are true or false. A reputable source indicates that with studying the student has a 90% chance of answering each question correctly. There are only three questions on the test. What is the probability that the student gets at least one question correct?
0.999
To find the probability that the student gets at least one question correct, we can use the concept of complementary probability.
To understand this, let's first find the probability that the student gets all questions wrong. Since each question has a 90% chance of being answered correctly, the probability of getting a question wrong is 1 - 0.9 = 0.1.
As all three questions are independent events, the probability of getting all three questions wrong is 0.1 * 0.1 * 0.1 = 0.001, which is 0.1% or 1/1000.
Now, to find the probability that the student gets at least one question correct, we subtract the probability of getting all questions wrong from 1. So the probability is 1 - 0.001 = 0.999, which is 99.9%.
Therefore, there is a 99.9% probability that the student gets at least one question correct on the exam.