Answer:
0.006% probability that the final vote count is unanimous.
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they vote yes, or they vote no. The probability of a person voting yes or no is independent of any other person. 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.
Random voting:
So 50% of voting yes, 50% no, so ![p = 0.5](https://tex.z-dn.net/?f=p%20%3D%200.5)
15 members:
This means that ![n = 15](https://tex.z-dn.net/?f=n%20%3D%2015)
What is the probability that the final vote count is unanimous?
Either all vote no(P(X = 0)) or all vote yes(P(X = 15)). So
![p = P(X = 0) + P(X = 15)](https://tex.z-dn.net/?f=p%20%3D%20P%28X%20%3D%200%29%20%2B%20P%28X%20%3D%2015%29)
In which
![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 = 0) = C_{15,0}.(0.5)^{0}.(0.5)^{15} = 0.00003](https://tex.z-dn.net/?f=P%28X%20%3D%200%29%20%3D%20C_%7B15%2C0%7D.%280.5%29%5E%7B0%7D.%280.5%29%5E%7B15%7D%20%3D%200.00003)
![P(X = 15) = C_{15,15}.(0.5)^{15}.(0.5)^{0} = 0.00003](https://tex.z-dn.net/?f=P%28X%20%3D%2015%29%20%3D%20C_%7B15%2C15%7D.%280.5%29%5E%7B15%7D.%280.5%29%5E%7B0%7D%20%3D%200.00003)
So
![p = P(X = 0) + P(X = 15) = 0.00003 + 0.00003 = 0.00006](https://tex.z-dn.net/?f=p%20%3D%20P%28X%20%3D%200%29%20%2B%20P%28X%20%3D%2015%29%20%3D%200.00003%20%2B%200.00003%20%3D%200.00006)
0.006% probability that the final vote count is unanimous.
Answer:
Step-by-step explanation:
the mean would be appropriate measure of center to describe the data shown in the histogram because the data is symmetrical.A symmetric histogram is a distribution in which the 2 halves appear to be the same on both sides.
Answer:
200 m.
Step-by-step explanation:
Step 1:
Length × Width = Area Equation
Step 2:
5 × 40 Multiply
Answer:
Area = 200
Hope This Helps :)