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ira [324]
3 years ago
11

40% of Oatypop cereal boxes contain a prize. Hannah plans to keep buying cereal until she gets a prize. What is the probability

that Hannah only to buy 3 or less boxes before getti g a prize? We need to design a simulation. Which random can we use to best represent this situation
Mathematics
2 answers:
aleksley [76]3 years ago
7 0

Answer:

(0.6)^{n}+n(0.4)(0.6)^{n-1}+\frac{n(n-1)(0.4)^{2}0.6^{n-2}}{2} +\frac{n(n-1)(n-2)0.4^{3}0.6^{n-3}}{6}

Step-by-step explanation:

We will use the binomial distribution. Let X be the random variable representing the no. of boxes Hannah buys before betting a prize.

Our success is winning the prize, p =40/100 = 0.4

Then failure q = 1-0.4  = 0.6

Hannah keeps buying cereal boxes until she gets a prize. Then n be no. times she buys the boxes.

P(X ≤ 3) = P(X=0) +P(X=1)+P(X=2)+P(X=3)

             = \binom{n}{0}p^{0}q^{n-0} +  \binom{n}{1}p^{1}q^{n-1}+ \binom{n}{2}p^{2}q^{n-2}+ \binom{n}{3}p^{3}q^{n-3}


             =  q^{n}+npq^{n-1}+\frac{n(n-1)(p)^{2}q^{n-2}}{2}+\frac{n(n-1)(n-2)p^{3}q^{n-3}}{6}

             = (0.6)^{n}+n(0.4)(0.6)^{n-1}+[tex]\frac{n(n-1)(0.4)^{2}0.6^{n-2}}{2} +\frac{n(n-1)(n-2)0.4^{3}0.6^{n-3}}{6}


zvonat [6]3 years ago
5 0

Answer:

Step-by-step explanation:

Use a random number generator ranging from 1-10......

You are welcome:)

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Solve the system ... y=3x-8 and y=-9x+4
natita [175]
1] y - 3x = -8
[2] y + 9x = 4

-3x + y = -8 9x + y = 4

Solve equation [2] for the variable y


[2] y = -9x + 4

// Plug this in for variable y in equation [1]

[1] (-9x+4) - 3x = -8
[1] - 12x = -12
// Solve equation [1] for the variable x


[1] 12x = 12

[1] x = 1
// By now we know this much :

y = -9x+4
x = 1
// Use the x value to solve for y

y = -9(1)+4 = -5

{y,x} = {-5,1}
7 0
2 years ago
The one-time fling! Have you ever purchased an article of clothing (dress, sports jacket, etc.), worn the item once to a party,
rjkz [21]

Answer:

a)  0.2725

b)  0.7275

c)  0.8948

Step-by-step explanation:

This is a binomial distribution probability problem. The formula is:

P(x)=\frac{n!}{(n-x)!x!}p^{x}q^{n-x}

Where

n is the number of trials [here we are taking 8 person, so n = 8]

x is what we are looking for [in the problem]

p is the probability of success [ 15%, so p = 0.15

q is the probability of failure [q = 1-p = 0.85]

Now,

a)

We are looking for "no one" did fling, so x = 0

Let's put into formula and find out the probability:

P(x=0)=\frac{8!}{(8-0)!0!}(0.15)^{0}(0.85)^{8}\\P(x=0)=0.2725

So, the probability that no one has done a one-time fling is 0.2725

b)

Atleast 1 person means P(x ≥ 1).

This can be found by:

P(x ≥ 1) = 1 - P(x=0) = 1 - 0.2725 = 0.7275

THus, Probability that at least one person has done a one-time fling is 0.7275

c)

No more than 2 people means P (x≤2).

This is essentially

P ( x ≤ 2 ) = P(x=0) + P(x=1) + P(x=2)

P ( x = 0 ) is found in part (a), which is 0.2725

P (x = 1 ) and P(x=2) can be found using formula:

P(x=1)=\frac{8!}{(8-1)!1!}(0.15)^{1}(0.85)^{7}\\P(x=1)=0.3847

and

P(x=2)=\frac{8!}{(8-2)!2!}(0.15)^{2}(0.85)^{6}\\P(x=2)=0.2376

Thus,

P ( x ≤ 2 ) = P(x=0) + P(x=1) + P(x=2) = 0.2725 + 0.3847 + 0.2376 = 0.8948

8 0
3 years ago
Someone help pls :((((
jasenka [17]

9514 1404 393

Answer:

  y +1 = -3(x -3)

Step-by-step explanation:

The given point is (3, -1), and the given slope is -3. The form suggests you want the point-slope form of the equation for the line:

  y -k = m(x -h) . . . . . . . . line with slope m through point (h, k)

Using the given values, the equation is ...

  y -(-1) = -3(x -3)

  y +1 = -3(x -3)

7 0
2 years ago
How many cubic centimeters of water can this paper cone cup hold?
RUDIKE [14]
By definition, the volume of a cone is given by:
 V = (1/3) * (pi) * (r ^ 2) * (h)
 Where,
 r: cone radius
 h: height of the cone
 Substituting values:
 V = (1/3) * (3.14) * ((8/2) ^ 2) * (9)
 V = 150.72 cm ^ 3

 Answer:
 this paper cone cup can hold:
 
V = 150.72 cm ^ 3
8 0
3 years ago
I don’t understand this problem
GuDViN [60]

z^2 - z - 72

z^2 - 9z + 8z - 72

<u>Step 1</u>: 72 = 9 * 8 and when we subtract -9+8 = -1 and that's how I went from z^2 - z - 72 to z^2 - 9z + 8z - 72.


<u>Step 2</u>: Taking out common value from first and second; and third and fourth.

z^2 - 9z = z(z - 9)

8z - 72 = 8 (z - 9)

z^2 - 9x + 8x - 72

z(z-9) + 8(z-9)

(z-9) (z+8)

4 0
3 years ago
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