1. Suppose that you just received a shipment of six televisions. Two of the TV's are defective.A) If two televisions are randomly selected, compute the probability that both televisions work B) What is the probability that at least one does not work?
2. Suppose that a box of 100 circuits is sent to a manufacturing plant. Of the 100 circuits shipped, 5 are defective. The plant manager receiving the circuits randomly selects 2 and tests them. If both work, she will accept the shipment. Otherwise the shipment's rejected. What is the probability that the plant manager discovers at least one defective circuit and rejects the shipment?
How do you solve these? the second one is explained in my textbook and they draw a diagram out I'm sorry but that's way to much to ask when I'm taking a timed test, plus the diagram makes no sense and they don't explain it well.
2. Suppose that a box of 100 circuits is sent to a manufacturing plant. Of the 100 circuits shipped, 5 are defective. The plant manager receiving the circuits randomly selects 2 and tests them. If both work, she will accept the shipment. Otherwise the shipment's rejected. What is the probability that the plant manager discovers at least one defective circuit and rejects the shipment?
How do you solve these? the second one is explained in my textbook and they draw a diagram out I'm sorry but that's way to much to ask when I'm taking a timed test, plus the diagram makes no sense and they don't explain it well.
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for such q's on draws w/o replacement, use combos
q1
P[both work] = 4c2/6c2 = 6/15 = 2/5 <-----
P[at least 1 doesn't work] = 1 - P[both work] = .......
q2
95 ok, 5 bad, 100 total
P[accepts shipment, ie both ok] = 95c2/100c2 = .9020
P[rejects, ie at least 1 bad] = 1 - .9020 = .098 <-----
q1
P[both work] = 4c2/6c2 = 6/15 = 2/5 <-----
P[at least 1 doesn't work] = 1 - P[both work] = .......
q2
95 ok, 5 bad, 100 total
P[accepts shipment, ie both ok] = 95c2/100c2 = .9020
P[rejects, ie at least 1 bad] = 1 - .9020 = .098 <-----
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thank goodness someone appreciates succinct answers !
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1. For the first TV, there is a 4/6 chance it works. For the second TV, there is a 3/5 chance it works. Hence, there is a 12/30 = 2/5 chance both work.
The probability at least one does not work = 1 - probability both work = 1 - 2/5 = 3/5
2. For the first randomly selected circuit, there is a 95/100 chance it works. For the second randomly selected circuit, there is a 94/99 chance it works. Hence, there is a (95*94)/(100*99) chance both circuits will work.
Therefore, the probability of a least one of the circuits being defective (and hence the shipment is rejected) = 1 - probability both work = 1 - (95*94)/(100*99)
The probability at least one does not work = 1 - probability both work = 1 - 2/5 = 3/5
2. For the first randomly selected circuit, there is a 95/100 chance it works. For the second randomly selected circuit, there is a 94/99 chance it works. Hence, there is a (95*94)/(100*99) chance both circuits will work.
Therefore, the probability of a least one of the circuits being defective (and hence the shipment is rejected) = 1 - probability both work = 1 - (95*94)/(100*99)