SOLUTION: A factory has 360 male workers and 640 female workers, with 100 male workers earning less than RM2000.00 a month and 170 female workers earning at least RM2000.00 a month. At the e

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Question 1171468: A factory has 360 male workers and 640 female workers, with 100 male workers earning less than RM2000.00 a month and 170 female workers earning at least RM2000.00 a month. At the end of the year, workers earning less than RM2000.00 are given a bonus of RM2000.00 whereas the others receive a bonus of a month's salary.
a. If two workers are randomly chosen, find the probability that only one worker
receives a bonus of RM2000.00.
b. If a male worker and a female worker are randomly chosen, find the probability that only one worker receives a bonus of RM2000.00.
Answer by CPhill(1959) About Me  (Show Source):
You can put this solution on YOUR website!
Let's break this problem down step-by-step.
**1. Organize the Data**
* Total Male Workers: 360
* Total Female Workers: 640
* Total Workers: 360 + 640 = 1000
* Male Workers Earning < RM2000: 100
* Male Workers Earning >= RM2000: 360 - 100 = 260
* Female Workers Earning >= RM2000: 170
* Female Workers Earning < RM2000: 640 - 170 = 470
**a. Probability of Only One Worker Receiving RM2000 Bonus (Two Randomly Chosen Workers)**
We need to consider two cases:
* Case 1: The first worker gets the RM2000 bonus, and the second worker doesn't.
* Case 2: The first worker doesn't get the RM2000 bonus, and the second worker does.
* **Case 1:**
* Probability of a worker getting RM2000 bonus: (100 + 470) / 1000 = 570 / 1000 = 0.57
* Probability of a worker NOT getting RM2000 bonus: (260 + 170) / 1000 = 430 / 1000 = 0.43
* Probability (Case 1): (570/1000) * (430/999)
* **Case 2:**
* Probability of a worker NOT getting RM2000 bonus: 430 / 1000 = 0.43
* Probability of a worker getting RM2000 bonus: 570 / 999
* Probability (Case 2): (430/1000) * (570/999)
* **Total Probability:**
* (570/1000) * (430/999) + (430/1000) * (570/999) = 2 * (570/1000) * (430/999)
* = 2 * (0.57) * (0.43043)
* = 0.490526
**b. Probability of Only One Worker Receiving RM2000 Bonus (One Male, One Female)**
We again have two cases:
* Case 1: The male worker gets the RM2000 bonus, and the female worker doesn't.
* Case 2: The male worker doesn't get the RM2000 bonus, and the female worker does.
* **Case 1:**
* Probability of a male worker getting RM2000 bonus: 100 / 360
* Probability of a female worker NOT getting RM2000 bonus: 170 / 640
* Probability (Case 1): (100 / 360) * (170 / 640)
* **Case 2:**
* Probability of a male worker NOT getting RM2000 bonus: 260 / 360
* Probability of a female worker getting RM2000 bonus: 470 / 640
* Probability (Case 2): (260 / 360) * (470 / 640)
* **Total Probability:**
* (100 / 360) * (170 / 640) + (260 / 360) * (470 / 640)
* = (17000 / 230400) + (122200 / 230400)
* = 139200 / 230400
* = 0.6041666666666667
* Approximately 0.6042