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In a survery of 200 employees of a compa...

In a survery of 200 employees of a company, it was found that 89 liked the lunch packs provided by the Company while the rest did not. Out of these employees, if one employee is chosen at random, what is the probability that the chosen employee:
(i) likes the lunch pack? (ii) dislikes the lunch pack?

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To solve the problem step by step, we will calculate the probabilities for both parts of the question. ### Step-by-Step Solution: 1. **Identify the Total Number of Employees:** - The total number of employees surveyed is given as 200. 2. **Identify the Number of Employees Who Liked the Lunch Packs:** - It is stated that 89 employees liked the lunch packs. 3. **Calculate the Number of Employees Who Disliked the Lunch Packs:** - To find the number of employees who disliked the lunch packs, we subtract the number of employees who liked the lunch packs from the total number of employees. - Number of employees who disliked the lunch packs = Total employees - Employees who liked lunch packs - Number of employees who disliked the lunch packs = 200 - 89 = 111 4. **Calculate the Probability That a Randomly Chosen Employee Likes the Lunch Pack:** - The probability (P) that a randomly chosen employee likes the lunch pack is given by the formula: \[ P(\text{likes lunch pack}) = \frac{\text{Number of employees who liked lunch packs}}{\text{Total number of employees}} \] - Substituting the values: \[ P(\text{likes lunch pack}) = \frac{89}{200} = 0.445 \] 5. **Calculate the Probability That a Randomly Chosen Employee Dislikes the Lunch Pack:** - The probability that a randomly chosen employee dislikes the lunch pack can be calculated as: \[ P(\text{dislikes lunch pack}) = 1 - P(\text{likes lunch pack}) \] - Substituting the value we found: \[ P(\text{dislikes lunch pack}) = 1 - 0.445 = 0.555 \] ### Final Answers: - (i) The probability that the chosen employee likes the lunch pack is **0.445**. - (ii) The probability that the chosen employee dislikes the lunch pack is **0.555**.
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