Answer:
The probability that you get zero questions correct is 0.4096
The probability that you get one questions correct is 0.4096
The probability that you get three questions correct is 0.0256
Step-by-step explanation:
These probability can be describe with a Binomial Distribution. These distribution can be used when we have n identical and independent situations in which there is a probability p or probability of success and a probability q or probability of fail. Additionally q is equal to 1 - p. The probability of x for a situation in which we can apply binomial distribution is:
![P( x,n,p) = n Cx * p^{x } * q^ {n-x}](https://tex.z-dn.net/?f=P%28%20x%2Cn%2Cp%29%20%3D%20n%20Cx%20%2A%20p%5E%7Bx%20%7D%20%2A%20q%5E%20%7Bn-x%7D)
Where x is the variable that says the number of success in the n situations
And nCx is calculate as:
![nC x = \frac{ n!}{ x! (n-x)! }](https://tex.z-dn.net/?f=nC%20x%20%3D%20%5Cfrac%7B%20n%21%7D%7B%20x%21%20%28n-x%29%21%20%7D)
From the question we can identify that:
- n is equal to 4 multiple choice question
- p is 1/5 or 0.2, the probability of get one question correct
- q is 4/5 or 0.8, the probability of get one question incorrect
Then the probability of get zero questions correct of 4 questions is:
![P( 0, 4, 0.2) = 4 C0 * p^{0 } * q^ {4-0}= 0.4096](https://tex.z-dn.net/?f=P%28%200%2C%204%2C%200.2%29%20%3D%204%20C0%20%2A%20p%5E%7B0%20%7D%20%2A%20q%5E%20%7B4-0%7D%3D%200.4096)
The probability of get one question correct of 4 questions is:
![P( 1, 4, 0.2) = 4 C1 * p^{1 } * q^ {4-1}= 0.4096](https://tex.z-dn.net/?f=P%28%201%2C%204%2C%200.2%29%20%3D%204%20C1%20%2A%20p%5E%7B1%20%7D%20%2A%20q%5E%20%7B4-1%7D%3D%200.4096)
The probability of get three questions correct of 4 questions is:
![P( 3, 4, 0.2) = 4 C3 * p^{3 } * q^ {4-3}= 0.0256](https://tex.z-dn.net/?f=P%28%203%2C%204%2C%200.2%29%20%3D%204%20C3%20%2A%20p%5E%7B3%20%7D%20%2A%20q%5E%20%7B4-3%7D%3D%200.0256)
Answer:
53% or 0.53 or 53/100
Step-by-step explanation:
9514 1404 393
Answer:
11
Step-by-step explanation:
The future value of the account is given by the formula ...
A = P(1 +r/12)^(12t) . . . . principal P invested at rate r for t years
Solving for t, we find ...
A/P = (1 +r/12)^(12t) . . . . . . . . . . . divide by P
log(A/P) = 12t·log(1 +r/12) . . . . . . take logs
Divide by the coefficient of t, then fill in the numbers.
t = log(A/P)/(12·log(1 +r/12)) = log(202800/93000)/(12·log(1 +.068/12))
t ≈ 11.497
It will take about 11 years for the account balance to reach the desired amount.
Answer:
Distance Maria had to walk in the afternoon is ![2\frac{7}{8}](https://tex.z-dn.net/?f=2%5Cfrac%7B7%7D%7B8%7D)
Step-by-step explanation:
Lets take that Maria walked
miles in the afternoon.
Distance walked in the morning + distance walked in the afternoon = ![10\frac{1}{8}](https://tex.z-dn.net/?f=10%5Cfrac%7B1%7D%7B8%7D)
⇒![7\frac{2}{8} +x=10\frac{1}{8}](https://tex.z-dn.net/?f=7%5Cfrac%7B2%7D%7B8%7D%20%2Bx%3D10%5Cfrac%7B1%7D%7B8%7D)
![\frac{58}{8} +\frac{8x}{8} =\frac{81}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B58%7D%7B8%7D%20%2B%5Cfrac%7B8x%7D%7B8%7D%20%3D%5Cfrac%7B81%7D%7B8%7D)
![\frac{58+8x}{8} =\frac{81}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B58%2B8x%7D%7B8%7D%20%3D%5Cfrac%7B81%7D%7B8%7D)
![58+8x=81](https://tex.z-dn.net/?f=58%2B8x%3D81)
![8x=81-58\\](https://tex.z-dn.net/?f=8x%3D81-58%5C%5C)
![8x=23](https://tex.z-dn.net/?f=8x%3D23)
![x=\frac{23}{8}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B23%7D%7B8%7D)
![x=2\frac{7}{8}](https://tex.z-dn.net/?f=x%3D2%5Cfrac%7B7%7D%7B8%7D)