Question

In a survey of 500 students, 50% like vanilla ice cream, 30% like chocolate ice cream, and 20% like both. Are the events P(like vanilla ice cream) and P(like chocolate ice cream) independent?

Option 1: Yes, because the classes are not the same
Option 2: Yes, because the intersection is not the sum of the individual probabilities
Option 3: No, because the intersection is not the sum of the individual probabilities
Option 4: No, because the intersection is not the same as the product of the individual probabilities

Answer 1

The events P(like vanilla ice cream) and P(like chocolate ice cream) are not independent because the intersection is not the same as the product of the individual probabilities.

Step-by-step explanation:

In order to determine whether the events P(like vanilla ice cream) and P(like chocolate ice cream) are independent, we need to compare the intersection of the two events to the product of the individual probabilities.

The intersection of the events is the percentage of students who like both vanilla and chocolate ice cream, which is 20%.

The product of the individual probabilities is the percentage of students who like vanilla ice cream multiplied by the percentage of students who like chocolate ice cream, which is (50%)*(30%) = 15%.

Since the intersection is not equal to the product of the individual probabilities, the events are not independent. Therefore, the correct option is No, because the intersection is not the same as the product of the individual probabilities.