An IKEA “Tarva” bed frame is assembled with screws and Allen wrenches. The screws and wrenches...

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An IKEA “Tarva” bed frame is assembled with screws and Allenwrenches. The screws and wrenches for the Tarva kits are grabbed atrandom from large bins at the factory by two different people whonever interact. Based on several years of data, it is known that95% of Tarvas come with the proper size Allen wrenches, and 85% ofthem come with the correct number of screws. Hints for the twoproblems below: It may help to write out the list of all possibleoutcomes of this random process. Also, remember that theprobabilities of outcomes add, and that independent probabilitiesmultiply.
(a) The bed frame can only be assembled if it contains theproper size Allen wrench and the correct number of screws. What isthe probability that your bed frame can be assembled?
(b) What is the probability that you have either the proper sizewrench or the correct number of screws, but not both?

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4.5 Ratings (760 Votes)

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

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