Ask question

Ask question

All categories

2 years ago

5

Suppose that a fair, 6 sided die is rolled. Let X indicate the event that an even number is rolled (in other words, X = 1 if an

even number is rolled and X = 0 otherwise). Let Y indicate the event that 2, 3, or 4 is rolled (in other words, Y = 1 if 2, 3, or 4 is rolled and Y = 0 otherwise). Find P (X = 0, Y = 1).

1 answer:

Sindrei [870]2 years ago

4 0

Answer: 1/2, 1/2

Step-by-step explanation:

A die has 6 faces.

Total number of faces = 6

Possible outcomes are :1,2,3,4,5,6

Even numbers : 2, 4, and 6 = 3

Non even numbers: 1,3,and 5= 3

First statement:

P(Even number) = 3/ 6 = 1/2

P(X=1) = 1/2

P(odd number) = 3/6 = 1/2

P(X=0) = 1/2

Second statement:

P(2) = 1/6

P(3) = 1/6

P(4) = 1/6

P(2 or 3 or 4) = (1/6) + (1/6) + (1/6)

P(2 or 3 or 4) = (1+1+1)/6 = 3/6 =1/2

Thus,

P(Y=1) = 1/2

Therefore,

P(X =0,Y=1) = 1/2, 1/2

You might be interested in

I WILL AWARD BRAINLIEST!! PLEASE HELP!!

bezimeni [28]

Answer:

Part 1) $A(57/7,9),B(4,16/5), m=7/5$

Part 2) $A(-7,6),B(9,-6/7), m=-3/7$

Part 3) $A(80/3,9),B(5,2.5), m=0.3$

Part 4) $A(-10/63,1/3),B(2/3,-22/90), m=-0.7$

Part 5) $A(-1/5,7),B(8,48), m=5$

Step-by-step explanation:

we know that

The equation of the line into slope intercept form is equal to

$y=mx+b$

where

m is the slope

b is the y-coordinate of the y-intercept

Part 1) we have

$7x-5y=12$

step 1

Find the slope

$7x-5y=12$

isolate the variable y

$y=(7/5)x-(12/5)$

so

the slope is $m=(7/5)$

step 2

Find the missing coordinate of point A

To find the x-coordinate of point A substitute the value of y-coordinate in the equation

$9=(7/5)x-(12/5)$

$(7/5)x=9+(12/5)$

$(7/5)x=(57/5)$

$x=(57/7)$

step 3

Find the missing coordinate of point B

To find the y-coordinate of point B substitute the value of x-coordinate in the equation

$y=(7/5)(4)-(12/5)$

$y=(28/5)-(12/5)$

$y=(16/5)$

Part 2) we have

$y=-(3/7)x+3$

step 1

Find the slope

the slope is $m=-(3/7)$

step 2

Find the missing coordinate of point A

To find the x-coordinate of point A substitute the value of y-coordinate in the equation

$6=-(3/7)x+3$

$(3/7)x=3-6$

$(3/7)x=-3$

$x=-7$

step 3

Find the missing coordinate of point B

To find the y-coordinate of point B substitute the value of x-coordinate in the equation

$y=-(3/7)(9)+3$

$y=-(27/7)+3$

$y=-(6/7)$

Part 3) we have

$y=0.3x+1$

step 1

Find the slope

the slope is $m=0.3$

step 2

Find the missing coordinate of point A

To find the x-coordinate of point A substitute the value of y-coordinate in the equation

$9=0.3x+1$

$0.3x=9-1$

$0.3x=8$

$x=80/3$

step 3

Find the missing coordinate of point B

To find the y-coordinate of point B substitute the value of x-coordinate in the equation

$y=0.3(5)+1$

$y=2.5$

Part 4) we have

$6.3x+9y=2$

step 1

Find the slope

$6.3x+9y=2$

isolate the variable y

$y=-(0.7)x+(2/9)$

so

the slope is $m=-0.7$

step 2

Find the missing coordinate of point A

To find the x-coordinate of point A substitute the value of y-coordinate in the equation

$(1/3)=-(0.7)x+(2/9)$

$(0.7)x=(2/9)-(1/3)$

$(0.7)x=(2/9)-(1/3)$

$(0.7)x=-(1/9)$

$x=-(10/63)$

step 3

Find the missing coordinate of point B

To find the y-coordinate of point B substitute the value of x-coordinate in the equation

$y=-(0.7)(2/3)+(2/9)$

$y=-(14/30)+(2/9)$

$y=-(22/90)$

Part 5) we have

$y-5x=8$

step 1

Find the slope

$y-5x=8$ -------> $y=5x+8$

the slope is $m=5$

step 2

Find the missing coordinate of point A

To find the x-coordinate of point A substitute the value of y-coordinate in the equation

$7=5x+8$

$5x=7-8$

$x=-1/5$

step 3

Find the missing coordinate of point B

To find the y-coordinate of point B substitute the value of x-coordinate in the equation

$y=5(8)+8$

$y=48$

6 0

2 years ago

The hypotenuse of a right triangle is 14 in. If the base

antoniya [11.8K]

Answer:

13.85

Step-by-step explanation:

U use the pythagorean theorem

So 2^2 + x^2 = 14^2

Simplify the equation: 4+x^2=196

--> x^2=192

--> x=13.85

-Hope this helps :)

8 0

1 year ago

Which table describes the behavior of the graph of f(x) = 2x3 – 26x – 24?

In-s [12.5K]

Answer:

For x∈ {-∞,-3} y<0, below x-axis

x∈ {-3,-1} y>0, above x-axis

x∈ {-1,4} y<0, below x-axis

x∈ {4,∞} y>0, above x-axis

Step-by-step explanation:

f(x)= $2x^{3}-26x-24$

$2x^{3}-26x-24$ =0

$2x^{3}-26x-24=0\\2x^{3}-2x-24x-24=0\\2x(x^{2} -1)-24(x+1)=0\\2x(x+1)(x-1)-24(x+1)=0\\(x+1)(2x^{2} -2x-24)=0\\=> x+1=0 => x_{1}=-1\\$

$=> 2x^{2} -2x-24=0\\=>2(x^{2} -x-12)=0\\=> x^{2} -x-12=0\\=> x^{2} -4x+3x-12=0\\=> x(x-4)+3(x-4)=0\\=> (x-4)(x+3)=0\\$

$=> x-4=0\\=> x_{2}=4\\=> x+3=0\\=>x_{3}=-3\\$

For x∈ {-∞,-3} y<0, below x-axis

x∈ {-3,-1} y>0, above x-axis

x∈ {-1,4} y<0, below x-axis

x∈ {4,∞} y>0, above x-axis

7 0

2 years ago

Read 2 more answers

The path traveled by a bottlenose dolphin as it jumps out of water is modeled by the equation y = −0.4x2 + 3x, where y is the he

Tamiku [17]

Answer:

5 feet

Step-by-step explanation:

The path traveled by a bottlenose dolphin as it jumps out of water is modeled by the equation,

$y=-0.4x^2+3x$

where y is the height above water and x is the horizontal distance in feet.

If a beam of light is shone upward at an angle modeled by the equation

$x+y=10$

A beam of light hit the dolphin.

So, line must be intersect path of dolphin.

Using substation method,

Substitute y=10-x into dolphin equation.

$10-x=-0.4x^2+3x$

$-0.4x^2+4x-10=0$

$x=\dfrac{-4\pm\sqrt{4^2-4(-10)(-0.4)}}{2(-0.4)}$

$x=5\text{ feet }$

$y=5\text{ feet }$

Hence, The beam hit dolphin at 5 feet.

8 0

2 years ago

Helena needs 3.5 cups of flour per loaf of bread and 2.5 cups of flour per batch of muffins. She also needs 0.75 cup of sugar pe

Arlecino [84]

From the given data, we can generate two equations with two unknowns.

We let x = number of loaves of bread
y = number of batches of muffins

For the equation of the flour requirement:
17 = 3.5x + 2.5y

<span>For the equation of the sugar requirement:
</span>4.5 = 0.75x + 0.75y

We evaluate the solutions by manipulating one of the equations into terms of the other. We use the first equation.We write x in terms of y.

x = (4.5/0.75) - y

Substitute the third equation to the second equation.

17 = (3.5((4.5/0.75)-y)) + 2.5y

Evaluating y and x, we have,

y = 4 and x = 2

Thus, from the amounts she has in hand, she can make 4 loaves of bread and 2 batches of muffins.

4 0

1 year ago

Read 2 more answers