Consider 4 classes, each consisting of 25 students

1. Consider 4 classes, each consisting of 25 students. From this group of 100 total students, a group of 4 students is to be chosen. (a) (1 point) How many choices are possible? (b) (1 point) How many choices are there in which all 4 students are in the same class? (c) (1 point) How many choices are there in which all of the 4 students are in different classes?2. Approximately 60% of U.S. households do not own a dog, and 70% do not own a cat. However, half of the households who own a cat also have at least one dog as a pet. Also, the ownership of cats and dogs are conditionally independent amongst households that own a horse. (a) (1 point) A U.S. household is picked at random. Is the probability that they own a cat independent of the probability that they own a dog? (b) (2 points) A U.S. household that owns a dog is chosen at random. What is the probability that they own a cat?

 

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