Final answer:
In Mathematics, when calculating the probability that Alan gets at least one out of 6 multiple choice questions correct by random guessing, we use the complement rule and find that the probability is 1 minus the probability of getting all questions wrong, which is 1 - (2/3)^6.
Step-by-step explanation:
The subject of this question is Mathematics, and it concerns the topic of probability, specifically with regards to multiple choice questions. The probability that Alan gets at least one of the 6 questions correct, when each question has 3 choices and he guesses randomly, can be calculated using the complement rule. The complement rule states that the probability of an event happening is 1 minus the probability of it not happening. So, we first find the probability that Alan gets all questions wrong and subtract that from 1.
The probability of getting one question wrong is 2/3, since there are 2 incorrect answers out of 3 possible choices. For Alan to get all 6 questions wrong, we raise this probability to the power of 6:
- Calculate the probability of getting one question wrong: 2/3.
- Calculate the probability of getting all 6 questions wrong: (2/3)^6.
- Subtract the probability of getting all questions wrong from 1: 1 - (2/3)^6.
After doing the calculations, we find that the probability of Alan getting at least one question correct is significantly higher than the probability of him getting all questions wrong.