A computer chip can be of two types: Defective (D) or Not-Defective (ND). There

Question

A computer chip can be of two types: Defective (D) or Not-Defective (ND). There are three companies A, B, and C that supply this chip. The proportion of Defectives if the item is supplied by company A, B, and C, are 0.1, 0.2, and 0.3 respectively. Companies A, B, and C provide 30%, 20% and 50% of a particular stock. If we randomly choose a chip from this stock and find it to be Defective, what is the probability that the chip comes from company B? A computer chip can be one of two types: Defective (D) or Not-Defective (ND). Given a chip, however, there is no easy way to tell whether it is Defective, but there is a test that can be applied to decide: The test gives + result, identifying the chip as Defective, with probability 0.9 if the chip is Defective. and +result with probability 0.1 if the chip is Not-Defective. I randomly select a chip from a population in which there are 10 Defective and 990 Not-Defective chips, apply the test on this selected chip, and get a +result. What is the probability that the chip is actually defective? In an experiment each of three vehicles takes a particular freeway exit turns left (L) or right (R) at the end of the exit ramp. List the outcomes in the compound events that: a) at leat one vehicle turns right, b all vechicles turn in the same direction. In a test, batteries come off an assembly line one by one until one having a voltage within prescribed limits is found. The probability of any particular battery being satisfactory is 0.99. List some simple events and find their probabilities. A system of five identical components are connected in series. Denote a component that fails by F and one that doesn't fail by S (for success). Let A be the event that the system fails. For A to occur, at least one of the individual components must fail. If the probability that each individual component fails is 0.9 independently of others, what is the probability that the system fails? A particular iPod playlist contains ten songs, two of which are by the Beatles. Suppose the shuffle feature is used to play the songs in random order (with equal probability and independent of each other). What is the probability that the first Beatles song heard is the fifth song played? Solar photovoltaic silicon cell arrays come in various configurations. In a system with six cells, three cells are connected in series to make a subsystem, the remaining three cells are connected in series to make another subsystem, and the two subsystems are connected to each other in parallel. The system

Explanation / Answer

P(B| Defective) = P(B and Defective)/P(Defective)

= (4/100)/(22/100) = 2/11

A B C Total Defective 0.1 * 30 = 3 0.2 * 20 = 4 0.3 * 50 = 15 22 Nondefective 30 - 3 = 27 20 - 4 = 16 50 - 15 = 35 100 - 22 = 78 Total 30 20 50 100

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