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Nat2105 [25]
3 years ago
12

How do I know when to use addition or subtraction when doing compound event probability?

Mathematics
1 answer:
Nitella [24]3 years ago
7 0

Addition Rule 1:

When two events, A and B, are mutually exclusive, the probability that A or B will occur is the sum of the probability of each event.

P(A or B) = P(A) + P(B)

Addition Rule 2:

When two events, A and B, are non-mutually exclusive, the probability that A or B will occur is:

P(A or B) = P(A) + P(B) - P(A and B)

In the rule above, P(A and B) refers to the overlap of the two events.

A student goes to the library. The probability that she checks out (a) a work of fiction is 0.40, (b) a work of non-fiction is 0.30, and (c) both fiction and non-fiction is 0.20. What is the probability that the student checks out a work of fiction, non-fiction, or both?

Solution: Let F = the event that the student checks out fiction; and let N = the event that the student checks out non-fiction. Then, based on the rule of addition:

P(F ∪ N) = P(F) + P(N) - P(F ∩ N)

P(F ∪ N) = 0.40 + 0.30 - 0.20 = 0.50

Subtraction Rule:

The probability that event A will occur is equal to 1 minus the probability that event A will not occur.

P(A) = 1 - P(A')

Suppose, for example, the probability that Bill will graduate from college is 0.80. What is the probability that Bill will not graduate from college? Based on the rule of subtraction, the probability that Bill will not graduate is 1.00 - 0.80 or 0.20.

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3 years ago
120 is what percent of 200
fredd [130]
The answer is 60% 
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Plan out an experiment that you could use to demonstrate experimental and theroretical probability
Murrr4er [49]

Answer:

Also, the more trials that you conduct in your experiment, the closer your calculations will be for the experimental and theoretical probabilities. The theoretical probability is 8.3% and the experimental probability is 4%. Although the experimental probability is slightly lower, this is not a significant difference.

Step-by-step explanation:

5 0
2 years ago
Find an equation of the tangent plane to the given surface at the specified point. z = ln(x − 8y), (9, 1, 0)
Archy [21]

Answer:

x - 8y - z = 1

Step-by-step explanation:

Data provided according to the question is as follows

f(x,y) = z = ln(x - 8y)

Now the equation for the tangent plane to the surface

For z = f (x,y) at the point P (x_0,y_0,z_0) is

z - z_0 = f_x(x_0,y_0)(x-x_0) + f_y(x_0,y_0)(y-y_0)\\

Now the partial derivatives of f are

f_x(x,y) = \frac{1}{x-8y} \\\\f_y(x,y) = \frac{8}{x-8y} \\\\P(x_0,y_0,z_0) = (9,1,0)\\\\f_z(9,1,0) = (\frac{1}{x-8y})_^{(9,1,0)}

\\\\=\frac{1}{9-8}

= 1

Now

f_y(9,1,0)=(\frac{8}{x-8y})_{(9,1,0)}\\\\ = -\frac{8}{9 - 8}

= -8

So, the tangent equation is

z - 0 = 1\times (x - 9) -8\times (y - 1)

Now after solving this, the following equation arise

z = x - 9 - 8y + 8

z = x - 8y - 1

Therefore

x - 8y - z = 1

4 0
3 years ago
I will give brainliest to first CORRECT answer.
astraxan [27]

Answer:

C. 576 ft.

Step-by-step explanation:

If the garden has a perimeter of 72feet and the lengths of each of the sides are lengthened by a factor of 8.

Perimeter of the enlarged garden = perimeter before enlargement x enlargement factor

That’s 72 x 8

576feet

7 0
3 years ago
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