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:
![9 < \sqrt{90} < 10](https://tex.z-dn.net/?f=9%20%3C%20%5Csqrt%7B90%7D%20%3C%2010)
Step-by-step explanation:
Since
and
, then ![9 < \sqrt{90} < 10](https://tex.z-dn.net/?f=9%20%3C%20%5Csqrt%7B90%7D%20%3C%2010)
10 to the 4th power is the answer.
1. do you realize you have Paul at the bottom of the paper, 2. Well, Its Paul, because it says “all the girls only have 1 pet and 1 brother or sibling,”