For this problem, the most accurate is to use combinations
Because the order in which it was selected in the components does not matter to us, we use combinations
Then the combinations are ![nC_r = \frac{ n! }{r! (n-r)!}](https://tex.z-dn.net/?f=%20nC_r%20%3D%20%5Cfrac%7B%20n%21%20%7D%7Br%21%20%28n-r%29%21%7D%20%20%20)
n represents the amount of things you can choose and choose r from them
You need the probability that the 3 selected components at least one are defective.
That is the same as:
(1 - probability that no component of the selection is defective).
The probability that none of the 3 selected components are defective is:
![P = \frac{_{117}C_3}{_{120}C_3}](https://tex.z-dn.net/?f=%20P%20%3D%20%5Cfrac%7B_%7B117%7DC_3%7D%7B_%7B120%7DC_3%7D%20%20%20)
Where
is the number of ways to select 3 non-defective components from 117 non-defective components and
is the number of ways to select 3 components from 120.
![_{117}C_3 = 260130](https://tex.z-dn.net/?f=%20_%7B117%7DC_3%20%3D%20260130%20%20)
![_{120}C_3 = 280840](https://tex.z-dn.net/?f=%20_%7B120%7DC_3%20%3D%20280840%20%20)
So:
![P = \frac{260130}{280840} = 0.927](https://tex.z-dn.net/?f=%20P%20%3D%20%5Cfrac%7B260130%7D%7B280840%7D%20%3D%200.927%20%20%20)
Finally, the probability that at least one of the selected components is defective is:
![P = 1-0.927 = 0.0737](https://tex.z-dn.net/?f=%20P%20%3D%201-0.927%20%3D%200.0737%20)
P = 7.4%
Answer:
48
Step-by-step explanation:
3.2 - 3 = .2
3(.2) = .6
9 + .6 = 9.6
5 * 9.6 = 48
Answer:
either 449/25 or 11/25 depends on the -14/5 or
Step-by-step explanation:
![- \frac{14}{25} or \: \frac{ - 14}{25}](https://tex.z-dn.net/?f=%20-%20%20%5Cfrac%7B14%7D%7B25%7D%20%20or%20%5C%3A%20%20%5Cfrac%7B%20-%2014%7D%7B25%7D%20)
if it the first one then the answer should be 449/25 but if ut the second one it should be 11/25 .
u just substitute the -14/5 to x then solve
Answer:
304,900
Step-by-step explanation:
186,000
88,900
304,900
Answer:
Speed of boat in still water is 6km/h
Speed of current is 4km/h
Step-by-step explanation:
We know speed = distance / time
Let the speed of boat in still water be x
Let the speed of current be y
Hence the speed of boat, down stream = ![x+y](https://tex.z-dn.net/?f=x%2By)
Distance downstream = 20km
Time taken = 2 hours
We have
![x+y=\frac{20}{2}](https://tex.z-dn.net/?f=x%2By%3D%5Cfrac%7B20%7D%7B2%7D)
......(1)
Speed of boat upstream = ![x-y](https://tex.z-dn.net/?f=x-y)
Distance upstream = 4
Time taken = 2
We have
![x-y=\frac{4}{2}](https://tex.z-dn.net/?f=x-y%3D%5Cfrac%7B4%7D%7B2%7D)
...(2)
Adding (1) & (2)
![2x=12](https://tex.z-dn.net/?f=2x%3D12)
![x=6](https://tex.z-dn.net/?f=x%3D6)
Substituting in (1) we get
![y=4](https://tex.z-dn.net/?f=y%3D4)