Thumbtacks A thumbtack is dropped on a concrete floor.

Chapter 12, Problem 12.1.267

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Thumbtacks A thumbtack is dropped on a concrete floor. Assume that the thumbtack can land only point up (u) or point down (d), as shown in the figure below. If two thumbtacks are dropped, one after the other, the tree diagram below can be used to show the possible outcomes. u u d d d u Sample Space First Thumbtack Second Thumbtack u u u d d u d d a) Do you believe that the outcomes of the thumbtack landing point up and the thumbtack landing point down are equally likely? Explain. b) List the sample points in the sample space of this experiment. c) Do you believe that the probability that both thumbtacks land point up (uu) is the same as the probability that both thumbtacks land point down (dd)? Explain. d) Can you compute the theoretical probability of a thumbtack landing point up and the theoretical probability of a thumbtack landing point down? Explain. e) Obtain a box of thumbtacks and drop the thumbtacks out of the box with care. Determine the empirical probability of a thumbtack landing point up when dropped and the empirical probability of a thumbtack landing point down when dropped.