Answer:
0.0025 = 0.25% probability that both are defective
Step-by-step explanation:
For each item, there are only two possible outcomes. Either they are defective, or they are not. Items are independent of each other. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
In which
is the number of different combinations of x objects from a set of n elements, given by the following formula.
![C_{n,x} = \frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=C_%7Bn%2Cx%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
And p is the probability of X happening.
5 percent of these are defective.
This means that ![p = 0.05](https://tex.z-dn.net/?f=p%20%3D%200.05)
If two items are randomly selected as they come off the production line, what is the probability that both are defective
This is P(X = 2) when n = 2. So
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
![P(X = 2) = C_{2,2}.(0.05)^{2}.(0.95)^{0} = 0.0025](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%20C_%7B2%2C2%7D.%280.05%29%5E%7B2%7D.%280.95%29%5E%7B0%7D%20%3D%200.0025)
0.0025 = 0.25% probability that both are defective
I believe it's C) 60 because ideally it would be 3 for every 25, 20 x 25 = 200, so then you would do 3 x 20 = 60
Perimeter of rectangle = 2(l+w)
So, 54cm = 2(l+9cm)
=> 54cm = 2l + 18cm
=> 54cm - 18cm = 2l
=> 36cm = 2l
=> 36cm/2 = l
=> 18cm = l
Answer: 360,000
Reason:
Think of 360 as 360.0
We move the decimal point 3 spots to the right to get to 360,000.0 or simply 360,000; this movement of 3 to the right is directly because of the exponent over the 10.
The 10^3 represents "thousand", so "360 x 10^3" is "360 thousand" = 360,000.
Only cabinet with two silver coins is cabinet B.
The chance of choosing cabinet B is 1/3.
Thus, there is a 1/3 chance of the two cabinets contain 2 silver coins.