E My Courses > CRN 40938 Score: 0 of 3 points An experiment consists of tossing a nickel, a dime, and a quarter. Of interest is the side the coin lands on. - List the sample space, separated each event by a comma. For example, HHT, HTH, etc. Enter your answer score: - Let \( A \) be the event that there are at least two tails. Find \( P(A) \). Enter your answer - Let \( B \) be the event that the first and second tosses land on tails. Are the events \( A \) and \( B \) mutually exclusive? A No, because \( P(A \) and \( B) \) is not equal to zero. B Yes, because \( P(A \) and \( B) \) is equal to zero. C Yes, because \( P(A \) and \( B) \) is not equal to zero. D No, because \( P(A \) and \( B) \) is equal to zero.

Let's break this down! First, the sample space for tossing a nickel (N), a dime (D), and a quarter (Q) can be represented as combinations of heads (H) and tails (T) for each coin: {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}. That's 8 possible outcomes! Next, for event \( A\) (at least two tails), we look for outcomes that have T appearing at least twice: {HTT, THT, TTH, TTT}. There are 4 favorable outcomes. Since the total outcomes are 8, \( P(A) = \frac{4}{8} = \frac{1}{2} \). Now, regarding events \( A \) and \( B\): \( B \) is the event that the first and second tosses land on tails. This means the outcomes would be {TTT, TTH}. Both events share some common outcomes (specifically TTT), which indicates that they are not mutually exclusive. So to answer the question, option A is correct: "No, because \( P(A \) and \( B) \) is not equal to zero." The outcomes and probabilities can come to life in so many fun ways! They not only help in understanding basic probability, but they also lay down the framework for more complex skills, such as predicting real-world scenarios or even playing games of chance skillfully! Exploring probability not only sharpens your analytical skills but is also a gateway into intriguing subjects like statistics, game theory, and even financial forecasting, and it can all be a lot of fun! Try tossing three coins yourself and see how many different patterns you can spot!