In Exercise 5, suppose that any incoming individual is equally likely to be assigned to any of the three stations irrespective of where other individuals have been assigned. What is the probability that a.? ll three family members are assigned to the same station? b.?? t most two family members are assigned to the same station? c.? very family member is assigned to a different station?

Answer : Step 1 of 3 : Given, any incoming individual is equally likely to be assigned to any of the three stations irrespective of where other individuals have been assigned. The sample space consists of all length three combinations, with repeats of the numbers 1, 2, and 3. For each of the three positions there are three possible choices, by using the product rule N = (3)(3)(3) = 27 a) The claim is to find the probability that all three family members are assigned to the same station. The are only 3 out of a possible 27 ways in which all members of the family go to the same station. P(all three family members are assigned to the same station) = 3/27 = 1/9 Step 2 of 3 : b) The claim is to find the probability that at most two family members are assigned to the same station. P(at most two family members are assigned to the same station) = 1 - P(all three family members are assigned to the same station) = 1 - 9 = 8/9