The answer to your question is 7/12
Answer: it’s 11 jk it’s 2
Step-by-step explanation:
Answer:
H
Step-by-step explanation:
I'm legit smart bro quit playing
Using the binomial distribution, it is found that there is a 0.0108 = 1.08% probability of the coin landing tails up at least nine times.
<h3>What is the binomial distribution formula?</h3>
The formula is:
![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)
![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)
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
In this problem:
- The coin is fair, hence p = 0.5.
- The coin is tossed 10 times, hence n = 10.
The probability that is lands tails up at least nine times is given by:
![P(X \geq 9) = P(X = 9) + P(X = 10)](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%209%29%20%3D%20P%28X%20%3D%209%29%20%2B%20P%28X%20%3D%2010%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 = 9) = C_{10,9}.(0.5)^{9}.(0.5)^{1} = 0.0098](https://tex.z-dn.net/?f=P%28X%20%3D%209%29%20%3D%20C_%7B10%2C9%7D.%280.5%29%5E%7B9%7D.%280.5%29%5E%7B1%7D%20%3D%200.0098)
![P(X = 10) = C_{10,10}.(0.5)^{10}.(0.5)^{0} = 0.001](https://tex.z-dn.net/?f=P%28X%20%3D%2010%29%20%3D%20C_%7B10%2C10%7D.%280.5%29%5E%7B10%7D.%280.5%29%5E%7B0%7D%20%3D%200.001)
Hence:
![P(X \geq 9) = P(X = 9) + P(X = 10) = 0.0098 + 0.001 = 0.0108](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%209%29%20%3D%20P%28X%20%3D%209%29%20%2B%20P%28X%20%3D%2010%29%20%3D%200.0098%20%2B%200.001%20%3D%200.0108)
0.0108 = 1.08% probability of the coin landing tails up at least nine times.
More can be learned about the binomial distribution at brainly.com/question/24863377
#SPJ1