All categories

2 years ago

Consider two events such that P(A)=3/4, P(B)=2/5 and P(AnB)=1/3. Are the events A and B independent?

1 answer:

6 0

If P(A) times P(B) is equal to P(A n B), then that shows the events are independent. Otherwise, they are dependent. When I write "A n B", I mean "A intersect B". The intersect symbol looks similar to the lowercase letter n.

P(A)*P(B) = (3/4)*(2/5) = (3*2)/(4*5) = 6/20 = 3/10

Since that result is not the same as P(A n B) = 1/3, this means that the events are not independent. They are dependent events. The answer is choice D

You might be interested in

What is the domain of the relation? {x| x = –4 , 0, 1, 2}. {x| x = –7, –6, 2, 11, 3}. {y| y = –4, 0, 1, 2}. {y| y = –7, –6, 2, 1

sukhopar [10]

Answer:

The correct answer B on ED

Step-by-step explanation:

5 0

2 years ago

Graph y=3x+1 by plotting two,points and connecting with a straight line

Vadim26 [7]

This is what the graph would look like

4 0

3 years ago

Which equation is a solution to (x-3)(x+9)=27?

Shtirlitz [24]

Answer:

x = ± $3\sqrt{7}$ - 3

Explanation:

I'm assuming you want the solutions to that equation, so here goes! (If not, please comment.)

(x-3)(x+9)=27

Let's FOIL this all out and expand. (Remember: First, Outer, Inner, Last.)

x^2 + 9x - 3x - 27

(first+ inner + outer + last)

x^2 + 9x - 3x - 27 = 27

Combine like terms, and add 27 to both sides.

x^2 + 6x - 27 + 27 = 27 + 27

x^2 + 6x = 54

Let's complete the square, because factoring doesn't work, and because it's good practice.

x^2 + 6x + ___ = 54 + ____

In the blank we will put b/2 ^2 = 6/2 ^2 = 3^2 = 9 to complete the square.

x^2 + 6x + 9 = 54 + 9

Now we've got a perfect square factor:

(x + 3)^2 = 63

sqrt(x+3)^2 = $\sqrt{63}$

x + 3 = ± $3\sqrt{7}$

x = ± $3\sqrt{7}$ - 3

7 0

2 years ago

Roberto must make his costume for his school play. He needs a piece of fabric that is 2 2/3 yards long and 1 1/2 yards wide. Wha

erik [133]

Answer:

He will need 8.34 yards of fabric.

Step-by-step explanation:

Given that,

The length of the fabric, l = 2 2/3 yards = 8/3 yards

The width of the fabric, b = 1 1/2 yards = 3/2 yards

We need to find the piece of fabric Roberto needs. It is equal to the perimeter of the fabric such that,

$P=2(l+b)\\\\P=2(\dfrac{8}{3}+\dfrac{3}{2})\\\\P=2\times \dfrac{25}{6}\\\\P=8.34\ \text{yards}$

So, he will need 8.34 yards of fabric.

7 0

2 years ago

Suppose customers in a hardware store are willing to buy N(p) boxes of nails at p dollars per box, as given by the following f

AleksAgata [21]

Answer:

a) -15 unites per dollar

b) -12 units per dollar

c) -18 units per dollar

Step-by-step explanation:

We are given the following in the question:

$N(p) = 100-3p^2, 1\leq p \leq 4$

where N(p) is the number of boxes of nails at p dollars per box.

a) average rate of change of demand for a change in price from $2 to $3.

Average rate of change =

$\displaystyle\frac{N(3) -N(2)}{3-2}\\\\=\frac{100-3(3)^2-(100 - 3(2)^2)}{1}\\\\= -15\text{ units per dollar}$

b) instantaneous rate of change of demand when the price is $2

Instantaneous rate =

$N'(p) = \displaystyle\frac{d(N(p))}{dp} = -6p$

$N'(2) = -6(2) = -12$

The instantaneous rate of change of demand when the price is $2 is decreasing at 12 units per dollar.

c) instantaneous rate of change of demand when the price is $3

Instantaneous rate =

$N'(3) = -6(8) = -18$

The instantaneous rate of change of demand when the price is $3 is decreasing at 18 units per dollar.

4 0

2 years ago