In a group of 200 car buyers, 60 bought alarm syatems, 50 bought heated seats, and 30 bought an alarm syetem and heated seata. Il a car buyer ehosen at random bought an alarm syetem, what is the probabilly thoy also bought heated seate? 25\% 50\% 20\% 2\% QUESTION is A POINTA How many words, with or without meaning, ean be formed using the letters in the word "WARRIOR'? 2401 49 5040 343

Let's address both of your questions one by one: --- ### **1. Probability Question** **Problem Statement:** In a group of 200 car buyers: - 60 bought alarm systems. - 50 bought heated seats. - 30 bought both an alarm system and heated seats. **Question:** If a car buyer chosen at random bought an alarm system, what is the probability they also bought heated seats? **Options:** - 25% - 50% - 20% - 2% **Solution:** We need to find the probability that a buyer who bought an alarm system also bought heated seats. This is a conditional probability problem, where we calculate \( P(\text{Heated Seats} \mid \text{Alarm System}) \). 1. **Total buyers who bought an alarm system (A):** 60 2. **Buyers who bought both alarm systems and heated seats (A ∩ H):** 30 The conditional probability formula is: \[ P(H \mid A) = \frac{P(A \cap H)}{P(A)} \] Plugging in the numbers: \[ P(H \mid A) = \frac{30}{60} = 0.5 \text{ or } 50\% \] **Answer:** **50%** --- ### **2. Permutation Question** **Problem Statement:** How many words, with or without meaning, can be formed using the letters in the word "WARRIOR"? **Options:** - 2401 - 49 - 5040 - 343 **Solution:** First, let's analyze the composition of the word "WARRIOR": - Total letters: 7 - Letters and their frequencies: - W: 1 - A: 1 - R: 3 - I: 1 - O: 1 Since there are repeating letters (specifically, the letter "R" appears 3 times), we'll use the formula for permutations of multiset: \[ \text{Number of distinct arrangements} = \frac{n!}{n_1! \times n_2! \times \ldots \times n_k!} \] Where: - \( n = \) total number of letters - \( n_1, n_2, \ldots, n_k = \) frequencies of each repeating letter Applying the values: \[ \text{Number of distinct arrangements} = \frac{7!}{3!} = \frac{5040}{6} = 840 \] However, **840** is not among the provided options. If we consider that there might be a typo and the word "WARRIOR" has only **two** "R"s instead of three, then: \[ \text{Number of distinct arrangements} = \frac{7!}{2!} = \frac{5040}{2} = 2520 \] Still, **2520** is not among the options either. Considering the closest possible answer provided: - **5040** is the value of \(7!\), which assumes all letters are distinct. Given the options and potential typographical errors in the question, **5040** seems to be the intended answer. **Answer:** **5040** --- If there's any discrepancy in the second question regarding letter repetitions, please double-check the word "WARRIOR" for accurate calculation.