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kvv77 [185]
3 years ago
10

in a final exam you have four multliple choice questions left to do. each questions has five suggested answers and only one of t

he answers in correct. assuming that your answers are randomly selected what is the probability that you get zero, one, or three questions correct?
Mathematics
1 answer:
kompoz [17]3 years ago
8 0

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}

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)! }

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

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

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

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Basically all you need to do is have 2 of the same digit next to each other.
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If UW = 4x – 1 and YZ = 5x + 4, what is UW?<br> (I need a answer and steps to stove)
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What do you mean what is UW ? There is no equation
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18 miles is what percent of 24 miles?
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Answer:

3/4

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M is the midpoint of segment GR. G has coordinates (11,-5) and M is (4,-4) Find the coordinates of R
7nadin3 [17]

Answer:

  • (3, -3)

Step-by-step explanation:

<u>Given:</u>

  • G = (11,-5)
  • M = (4,-4)
  • R = ?

<u>Solution</u>

  • R(x, y)

<u>As per midpoint formula;</u>

  • 4 = (11 + x)/2  ⇒ x + 11 = 8 ⇒ x = 3
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Find all points on the portion of the plane x+y+z=5 in the first octant at which f(x, y, z) = xy2z2 has a maximum value.
irina1246 [14]
Lagrange multipliers:

L(x,y,z,\lambda)=xy^2z^2+\lambda(x+y+z-5)

L_x=y^2z^2+\lambda=0
L_y=2xyz^2+\lambda=0
L_z=2xy^2z+\lambda=0
L_\lambda=x+y+z-5=0

\lambda=-y^2z^2=-2xyz^2=-2xy^2z

-y^2z^2=-2xyz^2\implies y=2x (if y,z\neq0)

-y^2z^2=-2xy^2z\implies z=2x (if y,z\neq0)

-2xyz^2=-2xy^2z\implies z=y (if x,y,z\neq0)

In the first octant, we assume x,y,z>0, so we can ignore the caveats above. Now,

x+y+z=5\iff x+2x+2x=5x=5\implies x=1\implies y=z=2

so that the only critical point in the region of interest is (1, 2, 2), for which we get a maximum value of f(1,2,2)=16.

We also need to check the boundary of the region, i.e. the intersection of x+y+z=5 with the three coordinate axes. But in each case, we would end up setting at least one of the variables to 0, which would force f(x,y,z)=0, so the point we found is the only extremum.
4 0
3 years ago
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