Answer:
a) P(X = 0) = 0.5997
b) P(X = 9) = 0.0016
c) P(X = 8) = 0.0047
d) P(X = 5) = 0.4018
Step-by-step explanation:
These following problem are examples of the binomial probability distribution.
Binomial probability
Th 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}.\pi^{x}.(1-\pi)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.%5Cpi%5E%7Bx%7D.%281-%5Cpi%29%5E%7Bn-x%7D)
In which
is the number of different combinatios 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
is the probability of X happening.
(a) for n = 4 and π = 0.12, what is P(X = 0)?
![P(X = 0) = C_{4,0}.(0.12)^{0}.(0.88)^{4} = 0.5997](https://tex.z-dn.net/?f=P%28X%20%3D%200%29%20%3D%20C_%7B4%2C0%7D.%280.12%29%5E%7B0%7D.%280.88%29%5E%7B4%7D%20%3D%200.5997)
(b) for n = 10 and π = 0.40, what is P(X = 9)?
![P(X = 9) = C_{10,9}.(0.4)^{9}.(0.6)^{1} = 0.0016](https://tex.z-dn.net/?f=P%28X%20%3D%209%29%20%3D%20C_%7B10%2C9%7D.%280.4%29%5E%7B9%7D.%280.6%29%5E%7B1%7D%20%3D%200.0016)
(c) for n = 10 and π = 0.50, what is P(X = 8)?
![P(X = 8) = C_{10,8}.(0.5)^{8}.(0.5)^{2} = 0.0047](https://tex.z-dn.net/?f=P%28X%20%3D%208%29%20%3D%20C_%7B10%2C8%7D.%280.5%29%5E%7B8%7D.%280.5%29%5E%7B2%7D%20%3D%200.0047)
(d) for n = 6 and π = 0.83, what is P(X = 5)?
![P(X = 5) = C_{6,5}.(0.83)^{5}.(0.17)^{1} = 0.4018](https://tex.z-dn.net/?f=P%28X%20%3D%205%29%20%3D%20C_%7B6%2C5%7D.%280.83%29%5E%7B5%7D.%280.17%29%5E%7B1%7D%20%3D%200.4018)
Answer:
4π
Step-by-step explanation:
We are asked to calculate the area of a circle whose diameter is equal to 4, we know that the area of the circle is given by the following equation:
A = π * (r ^ 2)
where r is the radius of the circle, we know that the radius of the circle is half the diameter, therefore:
r = d / 2 = 4/2
r = 2
replacing, we are left with:
A = π * (2 ^ 2)
A = 4π
Which means that the area of the circle is 4π
Answer:
length of its each side is 786 cm
Step-by-step explanation:
l² = 617796cm²
l = √617796
l = 786cm
Its asking how much did they both spent, in total, in order to reach the same amount spent in part A