Find the Y intercept of the graph

A coin, having probability p of landing heads, is continually flipped until at least one head and one tail have been flipped. (a

Natali [406]

Answer:

(a)

The probability that you stop at the fifth flip would be

$p^4 (1-p) + (1-p)^4 p$

(b)

The expected numbers of flips needed would be

$\sum\limits_{n=1}^{\infty} n p(1-p)^{n-1} = 1/p$

Therefore, suppose that $p = 0.5$ , then the expected number of flips needed would be 1/0.5 = 2.

Step-by-step explanation:

(a)

Case 1

Imagine that you throw your coin and you get only heads, then you would stop when you get the first tail. So the probability that you stop at the fifth flip would be

$p^4 (1-p)$

Case 2

Imagine that you throw your coin and you get only tails, then you would stop when you get the first head. So the probability that you stop at the fifth flip would be

$(1-p)^4p$

Therefore the probability that you stop at the fifth flip would be

$p^4 (1-p) + (1-p)^4 p$

(b)

The expected numbers of flips needed would be

$\sum\limits_{n=1}^{\infty} n p(1-p)^{n-1} = 1/p$

Therefore, suppose that $p = 0.5$ , then the expected number of flips needed would be 1/0.5 = 2.

7 0

2 years ago

A small Business earns a profit of $6500 in January and $17,500 in May. What is the rate of change in profit for this time perio

lukranit [14]

Answer:
Rate of change of profit for this period = $2750 / month

4 0

2 years ago

Rewrite the equation using the properties of exponents. <img src="https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B81y%5E7%7D"

nekit [7.7K]

Answer:

3y^2 3√3y(end route) if you are simplifying, and (81y^7)^1/3 if you are rewriting it.

Step-by-step:

I know this!

3 0

3 years ago

Please help. If you answer correctly and give an explanation I'll give you 5 stars, thanks, and brainliest.

timama [110]

The solution of the equation is $x=\frac{11}{7}$

Step-by-step explanation:

To simplify an equation of x

Simplify each side of the equation
Collect x in side and the numerical terms in the other side
Find the value of x

∵ The equation is $2x + \frac{1-x}{4}=3$

- Multiply all terms of the equation by 4 to cancel the denominator

of the 2nd term in the left hand side

∵ The equation is $4(2x) +4 (\frac{1-x}{4})=4(3)$

∴ 8x + (1 - x) = 12

∴ 8x + 1 - x = 12

- Add like terms

∴ (8x - x) + 1 = 12

∴ 7x + 1 = 12

- Subtract 1 from both sides

∴ 7x = 11

- Divide both sides by 7

∴ $x=\frac{11}{7}$

The solution of the equation is $x=\frac{11}{7}$

Learn more:

You can learn more about the solution of an equation in brainly.com/question/11306893

#LearnwithBrainly

3 0

2 years ago

A Travel Weekly International Air Transport Association survey asked business travelers about the purpose for their most recent

siniylev [52]

Answer:

(a) P (p' > 0.25) = 0.

(b) P (0.15 < p' < 0.20) = 0.7784.

(c) P (133 < X < 171) = 0.2205

Step-by-step explanation:

Let p = proportion of business trip that were for internal company visit.

It is provided that 19% responded that it was for an internal company visit, i.e.

p = 0.19.

A sample of n = 950 business travelers are randomly selected.

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

$\mu_{\hat p}=p$

The standard deviation of this sampling distribution of sample proportion is:

$\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}$

Thus, the distribution of $\hat p$ is N (μ = 0.19, σ = 0.013).

(a)

Compute the probability that more than 25% of the business travelers say that the reason for their most recent business trip was an internal company visit as follows:

P (p' > 0.25) = P (Z > 4.62) = 0

*Use a z-table for the probability.

Thus, the probability that more than 25% of the business travelers say that the reason for their most recent business trip was an internal company visit is 0.

(b)

Compute the probability that between 15% and 20% of the business travelers say that the reason for their most recent business trip was an internal company visit as follows:

P (0.15 < p' < 0.20) = P (-3.08 < Z < 0.77)

= P (Z < 0.77) - P (Z < -3.08)

= 0.7794 - 0.0010

= 0.7784

*Use a z-table for the probability.

Thus, the probability that between 15% and 20% of the business travelers say that the reason for their most recent business trip was an internal company visit is 0.7784.

(c)

Compute the proportion of X = 133 and X = 171 as follows:

p' = 133/950 = 0.14

p' = 171/950 = 0.18

Compute the value of P (0.14 < p' < 0.20) as follows:

P (0.14 < p' < 0.18) = P (-3.85< Z < -0.77)

= P (Z < -0.77) - P (Z < -3.85)

= 0.2206- 0.0001

= 0.2205

*Use a z-table for the probability.

Thus, the probability that between 133 and 171 of the business travelers say that the reason for their most recent business trip was an internal company visit is 0.2205.

7 0

3 years ago