An urn contains 75 marbles: 35 are blue, and 25 of these blue marbles are swirled. The rest of them are red, and 30 of the red ones are swirled. The marbles that are not swirled are clear. What is the probability of drawing:
- A blue marble from the urn?
- A clear marble from the urn?
- A blue, swirled marble?
- A red, clear marble?
- A swirled marble?
In this section, two expressions were developed for the probability of either of two events, A or B, occurring. Referring to Equations 4-2 and 4-3:
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An employee at Info tech enter product information into the computer. The employee may use a light pen that transmits the information to the PC along with keyboard to issue commands, or fill out a bubble sheet and feed it directly into the old mainframe. Historically, we know the following probabilities
P(light pen will fail) = 0.025
P(PC keyboard will fail) = 0.15
P(Light pen and PC keyboard will fail) = 0.005
P(Mainframe will fail) = 0.25
Data can be entered into the PC only if both the light pen and keyboard are functioning.
- What is the probability that the employee can use the PC to enter data?
- What is the probability that either the PC fails or the mainframe fails? Assume they cannot both fail at the same time.
The HAL Corporation wishes to improve the resistance of its personal computer to disk-drive and keyboard failures. At present, the design of the computer is such that disk-drive failures occur only one-third as often as keyboard failures. The probability of simultaneous disk-drive and keyboard failures is 0.05.
- If the computer is 80 percent resistant to disk-drive and/or keyboard failure, how low must the disk-drive failure probability be?
- If the keyboard is improved so that it fails only twice as often as the disk-drive (and the simultaneous failure probability is still 0.05), will the disk-drive failure probability from part (a) yield a resistance to disk-drive and/or keyboard failure higher or lower than 90 percent?
The Herr-McFee Company, which produces nuclear fuel rods,must X-ray and inspect each rod before shipping. Karen Wood, an inspector, has noted that for every 1,000 fuel rods she inspects, 10 have interior, flaws, 8 have casing flaws, and 5 have both flaws. In her quarterly report, karen must include the probability of flaws in fuel rods. What is this probability?
What is the probability that in selecting two cards one at a time from a deck with replacement, the second card is
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Sol O'Tarry, a prison administrator, has been reviewing the prison records on attempted escapes by inmates. He has data covering the last 45 years that the prison has been open, arranged by seasons. The data are summarized in the table.
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What is the probability that a couple's second child will be (a) A boy, given that their first child was a girl? (b) A girl, given that their first child was a girl?
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In rolling two dice, what is the probability of rolling (a) A total of 7 on the first roll, followed by a total of 11 on the second roll? (b) A total of 21 on the first two rolls combined? (c) A total of 6 on the first three rolls combined?
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A bag contains 32 marbles: 4 are red, 9 are black,12 are blue, 6 are yellow, and 1 is purple. Marbles are drawn one at a time with replacement. What is the probability that
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