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\"Estimation\" Problem: When my kids were younger, my family would take a three-

ID: 3251646 • Letter: #

Question

"Estimation" Problem:

When my kids were younger, my family would take a three-day trip to Disneyland about once every three years, probably not atypical for a family like ours that lives in California. We usually stayed at a nice, 2-bedroom unit in a suite hotel not too far from Disneyland, also probably not atypical for a family like ours. The week before we left on one of those trips we discovered that my sister- and brother-in-law and their three kids were going to be at Disneyland at the very same time, and were going to be staying in the very same hotel! We were amazed. So first, estimate the chance of that happening. And also, should we have been as surprised as we were?

Explanation / Answer

No of weeks in 3 years = 3*52 = 156

Hence the sister and brother in law and their kids could go on any week out of the 156 weeks. Hence probability that they too travel in the same week = 1/156

Having the same hotel depends on the number of hotels in the vicinity of Disneyland. Let us say there are 40 hotels in the vicinity of Disneyland. Then the probability of having hte same hotel = 1/40

Hence combined probability = 1/156*1/40 = 1/6240

This probability is quite low and hence being surprised is expected.