Question

1. An IKEA “Tarva” bed frame is assembled with screws and Allen wrenches. The screws and wrenches for the Tarva kits are grabbed at random from large bins at the factory by two different people who never interact. Based on several years of data, it is known that 95% of Tarvas come with the proper size Allen wrenches, and 85% of them come with the correct number of screws. Hints for the two problems below: It may help to write out the list of all possible outcomes of this random process. Also, remember that the probabilities of outcomes add, and that independent probabilities multiply.

   1. (a) The bed frame can only be assembled if it contains the proper size Allen wrench and the correct number of screws. What is the probability that your bed frame can be assembled?

   2. (b) What is the probability that you have either the proper size wrench or the correct number of screws, but not both?

Answer 1

P(proper size wrench) = 0.95

P(correct number of screws) = 0.85

a) P(proper size wrench and correct number of screws) = P(proper size wrench) * P(correct number of screws)

                                                                                         = 0.95 * 0.85

                                                                                         = 0.8075

b) P(either the proper size wrench or the correct number of screws, but not both) = P(only proper size wrench) + P(only correct number of screws)

                                                              = (P(proper size wrench) - P(proper size wrench and correct number of screws)) + (P(correct number of screws) - P(proper size wrench and correct number of screws))

                                                              = (0.95 - 0.8075) + (0.85 - 0.8075)

                                                              = 0.185