In a large retirement community, 60% of households have no dogs, 30% have one dog, and 10% have two dogs. Following a news story about how the elderly have trouble walking their dogs in the winter weather, a magnanimous group of teenagers decides that it will randomly select two households in the retirement community each and call and offer to walk their dog(s). For each teen who participates, T is the total number of dogs in the two households called.
a. List all possible values for T.
b. Find the sampling distribution for T. (Hint: This is simply a list of possible values for T and their probabilities.)
c. If there are no dogs in the two households (T = 0), the teen starts over with a new sample of two households. If 1000 teens participate, for about how many of them will T = 0 for their first sample?