All categories

3 years ago

If A and B are independent events, then it must be true that P(A|B)=P(A)?

Mathematics

1 answer:

nataly862011 [7]3 years ago

7 0

Answer:

True : If A and B are independent events, then P(A|B)=P(A) is true.

Step-by-step explanation:

If A and B are independent, P(A and B) = P(A) * P(B)

P(A|B) conditional probability, P(A) given B has already happened

= P(A and B) / P(B)

= P(A)*P(B) / P(B)

= P(A)

Therefore

If A and B are independent events, P(A|B)=P(A) is true.

You might be interested in

II. Let f(x) = 9 – x , g(x) = x2 + x, and h(x) = x – 2. Compute the following:

Neko [114]

Answer:

$h(g(x))=x^2+x-2$

$h(g(f(x))= x^2-19x+88$

Step-by-step explanation:

<u>Composite Function</u>

Suppose f(x) and g(x) are real functions, the composite function named $(f\circ g)(x)$ is defined as:

$(f\circ g)(x)=f(g(x))$

The composite function can be found by substituting g into f.

We are given these functions:

$f(x)=9-x$

$g(x)=x^2+x$

$h(x)=x-2$

Find:

a) h(g(x))

Substituting g into h:

$h(g(x))=x^2+x-2$

b) h(g(f(x))

First we find g(f(x)):

$g(f(x))=(9-x)^2+(9-x)$

Operating:

$g(f(x))=81-18x+x^2+9-x$

Simplifying:

$g(f(x))=90-19x+x^2$

Now find h(g(f(x)) replacing the above equation into h:

$h(g(f(x))= 90-19x+x^2-2$

Simplifying and rearranging:

$h(g(f(x))= 88-19x+x^2$

$h(g(f(x))= x^2-19x+88$

3 0

3 years ago

Can the volume of a cone with the same size base as a cylinder ever have a bigger volume? Explain

Liono4ka [1.6K]

Answer:

No, because if a cone and a cylinder have bases with equal areas, and both have identical heights, then the volume of the cone is one-third the volume of the cylinder.

3 0

3 years ago

How many different types of cross sections of a cone are possible?. A. 3. B. 5. C. 6. D. 10

Rama09 [41]

6 different types of cross sections of a cone are possible.

8 0

4 years ago

Use the first derivative of the following <br><img src="https://tex.z-dn.net/?f=f%28x%29%20%5Cfrac%7B1%7D%7Bx%20-%201%7D%20" id=

Olenka [21]

Answer:

f (x)=−(x−1)−2

Step-by-step explanation:

6 0

3 years ago

Which of the following is most likely the next step in the series?

Nostrana [21]

Answer:

A is most likely the next step in the series

Step-by-step explanation:

Each step, the number of sides is increasing by 1.

4,5,6 means that the next number of sides would be 7. Option A has 7 sides.

8 0

3 years ago