Question 1176389
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**