suppse you received a shipment of nine televisions. four of the television are defective. If two televisions are random;y selected compute the probability at least on of the two televisions does not work
Let
D=event that a television selected is defective
and
~D=event that a television selected is NOT defective
Then probability that both are not defective:
P(~D~D)=(5/9)(4/8)=5/18
Therefore at least one defective is its complement
P( (~D~D)') = 1-5/18 = 13/18
Suppose you just received a shipment of tenten televisions. TwoTwo of the televisions are defective. If two televisions are randomly selected, compute the probability that both televisions work. What is the probability at least one of the two televisions does not work?
To find the probability that at least one of the two televisions does not work, we can calculate the probability of the opposite scenario (both televisions work) and subtract it from 1.
Given that the total number of televisions is 9 and 4 of them are defective, the probability that the first television selected works is:
P(works) = (Number of working televisions)/(Total number of televisions)
= (9 - 4)/(9)
= 5/9
Once we have selected a working television, there are now 8 televisions remaining, with 3 defective ones. Therefore, the probability that the second television selected works is:
P(works) = (Number of working televisions)/(Total number of televisions)
= (8 - 3)/(8)
= 5/8
To find the probability that both televisions work (opposite scenario), we multiply these probabilities together:
P(both work) = P(works for first television) * P(works for second television)
= (5/9) * (5/8)
= 25/72
Finally, the probability that at least one of the two televisions does not work is:
P(at least one does not work) = 1 - P(both work)
= 1 - 25/72
= 47/72
Therefore, the probability that at least one of the two televisions does not work is 47/72.
To compute the probability that at least one of the two randomly selected televisions does not work, we can use the concept of complementary probability.
First, let's calculate the probability that both selected televisions work. To do this, we need to find the probability of selecting a working television for the first pick and then for the second pick.
The probability of selecting a working television on the first pick is given by:
P(working on first pick) = (number of working televisions) / (total number of televisions)
= (9 - 4) / 9
= 5 / 9
After the first pick, there are 8 televisions left, 4 of which are defective.
The probability of selecting a working television on the second pick, given that the first pick was successful, is given by:
P(working on second pick | working on first pick) = (number of working televisions remaining) / (total number of remaining televisions)
= (5 - 1) / 8
= 4 / 8
= 1 / 2
To find the probability that both selected televisions work, we need to multiply the probabilities of each pick:
P(both working) = P(working on first pick) * P(working on second pick | working on first pick)
= (5 / 9) * (1 / 2)
= 5 / 18
The probability that at least one of the two selected televisions does not work is the complementary probability of both selected televisions working. Therefore:
P(at least one not working) = 1 - P(both working)
= 1 - (5 / 18)
= (18 - 5) / 18
= 13 / 18
So, the probability that at least one of the two randomly selected televisions does not work is 13/18.