Another game you’ve set up at casino night involves rolling a fair six-sided die followed by tossing a fair coin. In this game, players earn points depending on the number they get on the die and which side of the coin turns up. For example, the player earns 5 points for getting (2, tails) Question 5 Find the probability that the outcome is either tails with any number, or heads with a number grater than 1

Answer:

a) 0.3087 = 30.87% probability that exactly two iPhones will end up being serviced under warranty.

b) 0.4718 = 47.18% probability that at least two iPhones will end up being serviced under warranty

c) The expected number of iPhones in the family that require service is 1.5.

d) The standard deviation of the number of iPhones in the family that requires service is 1.0247.

Step-by-step explanation:

For each iPhone, there are only two possible outcomes. Either they have battery issues under warranty, or they do not. iPhones are independent. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Thirty percent of such iPhones will need battery service while under warranty.

This means that [tex]p = 0.3[/tex]

A family owns 5 iPhones produced within the time frame of potential faulty production.

This means that [tex]n = 5[/tex]

(a) What is the probability that exactly two iPhones will end up being serviced under warranty?

This is P(X = 2).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{5,2}.(0.3)^{2}.(0.7)^{3} = 0.3087[/tex]

0.3087 = 30.87% probability that exactly two iPhones will end up being serviced under warranty.

(b) What is the probability that at least two iPhones will end up being serviced under warranty?

This is:

[tex]P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)[/tex]

So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{5,2}.(0.3)^{2}.(0.7)^{3} = 0.3087[/tex]

[tex]P(X = 3) = C_{5,3}.(0.3)^{3}.(0.7)^{2} = 0.1323[/tex]

[tex]P(X = 4) = C_{5,4}.(0.3)^{4}.(0.7)^{1} = 0.0284[/tex]

[tex]P(X = 5) = C_{5,5}.(0.3)^{5}.(0.7)^{0} = 0.0024[/tex]

[tex]P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.3087 + 0.1323 + 0.0284 + 0.0024 = 0.4718[/tex]

0.4718 = 47.18% probability that at least two iPhones will end up being serviced under warranty.

(c) What is the expected number of iPhones in the family that require service?

[tex]E(X) = np = 5*0.3 = 1.5[/tex]

The expected number of iPhones in the family that require service is 1.5.

(d) What is the standard deviation of the number of iPhones in the family that requires service?

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{5*0.3*0.7} = 1.0247[/tex]

The standard deviation of the number of iPhones in the family that requires service is 1.0247.

Answer:

( x +1 ) ( x + 3 )

Answer:

No

Step-by-step explanation:

In order for the shapes to be congruent, corresponding parts must be congruent.  The corresponding angles are NOT congruent, so the shapes are not congruent.

Answer:

The lines will never intersect.Step-by-step

explanation:

The slope of the cups is the same, 1.5.  The y-intercept of the small cups is 6The y-intercept of the big cups is 9. This means that the lines will never intersect because they are parallel lines and have the same slope but different y-intercepts.

I hope this helps :)   Please give brainliest! :)

Answer:

y = -5x + 12

Step-by-step explanation:

slope intercept form is where you simplify it and get the y by itself, so:

[tex]y-2 = -5(x-2)\\y-2 = -5x+10\\y = -5x+ 12[/tex]

Answer:

I cannot see the question clearly. But I know how to do .

Answer:

4800 1 x 24 x 25 x 8

Step-by-step explanation: 1 x 24 x 25 x 8

Answer:

I just did it its 1/3n - 5

Step-by-step explanation:

Answer:

$9.90

Step-by-step explanation:

$2.97 divided by 3 equal 0.99 cents

0.99 multiplied by 10 equal 9.90

Answer:

a= x= 3, -1

b= x=1

c= (1, -8)

Step-by-by-step explanation:

For the show your work, you have to create the graph of the parabola. (attached image)

Answer:

270

Step-by-step explanation:

bc if he does 9 miles for 3 days every week thats already 27 miles. for 10 weeks that would be 270 bc 10*27 is 270.

Answer:

y=x-4

Step-by-step explanation:

Answer:

-9/5 is the slope

Step-by-step explanation:

5-(-4)=9

1-6=-5

Answer:

Step-by-step explanation:

From the first image attached below, we will see the sketch of the curve x = y² & x = 2y

In the picture connected underneath, the concealed locale(shaded region) is bounded by the given curves. Now, we discover the marks of the crossing point of the curves. These curves will cross, when:

[tex]y^2 =2 y \\ \\ or y^2 -2y = 0 \\ \\ y(y-2) = 0 \\ \\ y = 0 \ \ or \ \ y = 2[/tex]

Thus, the shaded region fall within the interval 0 ≤ y ≤ 2

Now, from the subsequent picture appended we sketch the solid acquired by turning the concealed region about the y-axis.

For the cross-sectional area of the washer:

[tex]A (y) = \pi (outer \ radius)^2 - \pi ( inner \ radius )^2 \\ \\ A(y) = \pi (2y^)2- \pi (y^)^2 \\ \\ A(y) = 4 \pi y^2 - \pi y^4 \\ \\ A(y) = \pi( 4 y^2 -y^4)[/tex]

Finally, the volume of (solid) is:

[tex]V = \int^2_0 A(y) \ dy \\ \\ V = \int^2_0 \pi (4y^2 -y^4) \ dy \\ \\ V = \pi \int^2_0 (4y^2 -y^4) \ dy \\ \\ V = \pi \Big[\dfrac{4}{3}y^3 - \dfrac{y^5}{5} \big ] ^2_0 \\ \\ V = \pi \Big [ \dfrac{4}{3}(2)^3-\dfrac{2^3}{5} \Big ] \\ \\ V = \dfrac{64}{15}\pi \\ \\ V = (4.27 ) \pi[/tex]

Answer:

5x-15 = 2x+21

x=12

Step-by-step explanation:

Vertical and Corresponding Angles can be used to prove so.

Answer:

the domain and range are all real numbers

Step-by-step explanation:

Answer:

x= 7y+14  /2

y= 2/ 7 x−2

Step-by-step explanation:

Answer:

10/20

Step-by-step explanation:

$15 for 10 hours and $20 for 10 hours

Answer:

Yes.

Step-by-step explanation:

Answer:

x is 21. dccxpxpdpdpdpdp

Answer:

Mutual

Step-by-step explanation:

33° +2x-15 =90

2x =90+15-33

2x=72

X=36

Answer:

95

Step-by-step explanation:

3x + x = 380

4x = 380

x= 95

proof

3*95 = 285

Your share of 285 plus that of your friend shares of 95 will give you the total shares of 380

Answer:

5²+1×2 - 4(4) = 11

Step-by-step explanation:

up top when it says a = 4

and b = 5 that's means b and a are those numbers.

then while 4 is touching a that means to multiply. And the 2 up top of b means 5×5, then do order of operations to find the answer. If you dont you'll get it WRONG.

Order of operations is this

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Answer:

1

Hope this helps!!!!

9514 1404 393

Answer:

  A, C, B

Step-by-step explanation:

It is helpful to remember the trig identities ...

  sin = 1/csc

  cos = 1/sec

  tan = 1/cot

__

1. sin(θ)cos(θ)sec(θ)csc(θ) = (sin(θ)csc(θ))(cos(θ)sec(θ)) = (1)(1) = 1 . . . matches A

2. 1/cot²(θ)·sec(θ)cos(θ) = 1/(1/tan²(θ))·(1) = tan²(θ) . . . matches C

3. tan(θ)/cot(θ) = tan(θ)/(1/tan(θ)) = tan²(θ) . . . matches B

Answer:

1.sin Θ cos Θ sec Θ csc Θ

sinocoso×1/coso ×1/sino=1

1. is the required answer

2.1/(cot^2Θ) * sec Θ cos Θ

=sin²o/cos²o×1/coso×coso

=sin²o/cos²o

tan²o is answer

3.tan Θ/ cot Θ

sino/coso/(coso/sino)

sin²o/cos²o

tan²ois answer here o = theta

Answer:

I think

A:(2,1)

B:(4,-2)

C:(4,-6)

D:(1,-3)

Step-by-step explanation:

[tex]f(\pi) = - 3 \\ f( \frac{\pi}{2} ) = 0 \\ f( - \frac{3\pi}{2} ) = 0 \\ \: \: = 3 \cos(theta) [/tex]

Answer:

Option A : The system has two solutions, and both are viable because they result in positive values of time.

Step-by-step explanation:

Answer:

the answer is A

Step-by-step explanation:

The system has two solutions, and both are viable because they result in positive values of time.