Question 1176389: 1.A survey classified a group of 100 students by sex and according to whether they prefer coco - cola or other brands of soft drink . The proportions falling into the four resulting categories are shown in the accompanying table . ( overline C ) Other brands .14 12 Prefers Sex Coco - Cola ( C ) Boy .44 Girl .30 If a single student is selected from a large group , find the probabilities the events as detailed below : a ) The student is a girl . b ) The student is a boy but does not prefer Coco - Cola c ) The student prefers coco - cola irrespective of Given that the selected student is a girl , what is the probability that she does not prefer Coco - Cola ?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's break down this probability problem.
**Given Information:**
| Sex | Coco-Cola (C) | Other Brands (C̄) |
|------|----------------|-------------------|
| Boy | 0.44 | 0.14 |
| Girl | 0.30 | 0.12 |
**Total Students:** 100
**a) The student is a girl.**
To find the probability of selecting a girl, we add the probabilities of girls preferring Coco-Cola and girls preferring other brands:
* P(Girl) = P(Girl, C) + P(Girl, C̄)
* P(Girl) = 0.30 + 0.12
* P(Girl) = 0.42
**b) The student is a boy but does not prefer Coco-Cola.**
This is directly given in the table:
* P(Boy, C̄) = 0.14
**c) The student prefers coco-cola irrespective of sex.**
To find the probability of a student preferring Coco-Cola, we add the probabilities of boys and girls preferring Coco-Cola:
* P(C) = P(Boy, C) + P(Girl, C)
* P(C) = 0.44 + 0.30
* P(C) = 0.74
**d) Given that the selected student is a girl, what is the probability that she does not prefer Coco-Cola?**
This is a conditional probability. We want to find P(C̄ | Girl).
* P(C̄ | Girl) = P(Girl, C̄) / P(Girl)
* P(C̄ | Girl) = 0.12 / 0.42
* P(C̄ | Girl) = 12 / 42
* P(C̄ | Girl) = 2 / 7
* P(C̄ | Girl) ≈ 0.2857
**Answers:**
* **a) P(Girl) = 0.42**
* **b) P(Boy, C̄) = 0.14**
* **c) P(C) = 0.74**
* **d) P(C̄ | Girl) ≈ 0.2857**
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