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mr_godi [17]
3 years ago
6

A gambler has a fair coin and a two-headed coin in his pocket. He selects one of the coins at random. (a) When he flips the coin

, what is the probability that it will show heads? (b) The coin shows heads. Now what is the probability that it is the fair coin?
Mathematics
1 answer:
Aleks04 [339]3 years ago
8 0

Answer:

a) probability of choosing heads= 1/2 (50%)

b)  probability of choosing the fair coin knowing that it showed heads is= 1/3 (33.33%)

Step-by-step explanation:

Since the unfair coin can have 2 heads or 2 tails , and assuming both are equally possible . then

probability of choosing the fair coin  (named A)= 1/2

probability of choosing an unfair coin with 2 heads (named B)= (1-1/2)*1/2= 1/4

probability of choosing an unfair coin with 2 tails (named C)= (1-1/2)*(1-1/2)= 1/4

then

probability of choosing heads= probability of choosing A * probability of getting heads from A + probability of choosing B * probability of getting heads from B + probability of choosing C * probability of getting heads from C =

1/2*1/2 + 1/4*1 + 1/4*0 = 2/4 = 1/2

the probability of choosing the fair coin knowing that it showed heads is

P(A/B) = P(A∩B)/P(B)

denoting event A= the coin is fair and event B= the result is heads

P(A∩B) = 1/2*1/2 = 1/4

but since we know now that that the unfair coin is not possible , the probability of choosing heads is altered:

P(B)=probability of choosing heads= probability of choosing A * probability of getting heads from A + probability of choosing B * probability of getting heads from B  = 1/2*1/2+1/2*1 = 3/4

then

P(A/B) = P(A∩B)/P(B)  = (1/4)/(3/4) = 1/3

then the probability is 1/3

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Factor the expression completely -15t-6
serg [7]

Answer:

\large\boxed{-15t-6=-3(5t+2)}

Step-by-step explanation:

-15t-6=(-3)(5t)+(-3)(2)=-3(5t+2)

6 0
3 years ago
Find the equation of a line parallel to 2x-2y=-4 that passes through the<br> point (3,9).
erastovalidia [21]

The line which is parallel to 2x-2y=-4 that passes through the

point (3,9) is x-y = -6.

Given that, 2x-2y = -4 passes through the point (3,9) then we have to find the equation of a line which is parallel to the given equation of line.

Let's proceed to find the equation of the line.

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis).

Using the slope-intercept formula, the equation of the line is:

y = mx + b

where,

m = the slope of the line

b = y-intercept of the line

(x, y) represent every point on the line

x and y have to be kept as the variables while applying the above formula.

2x-2y = -4

-2y = -4-2x

y = -4/-2 - 2x/-2

y = 2+x

y = x+2

On comparing with y = mx+b

m = 1 and b = 2

As the lines are parallel then the slope of other line will also be same i.e., m = 1

The point from which it is passes is (3,9)

⇒ x₁ = 3 and y₁ = 9

y-y₁ = m(x-x₁)

⇒ y-9 = 1(x-3)

⇒ y-9 = x-3

⇒ y = x-3+9

⇒ y = x+6

⇒ x-y = -6

Therefore, the line which is parallel to 2x-2y=-4 that passes through the

point (3,9) is x-y = -6.

Hence, x-y = -6 is the required answer.

Learn more in depth about similar problem at brainly.com/question/1884491

#SPJ1

7 0
1 year ago
A marketing researcher wants to find a 96% confidence interval for the mean amount those visitors spend per person per day while
ki77a [65]

Answer:

n=(\frac{2.054(12)}{4})^2 =37.97 \approx 38

So then the minimum sample to ensure the condition given is n= 38

Step-by-step explanation:

Notation

\bar X represent the sample mean for the sample  

\mu population mean (variable of interest)

\sigma=12 represent the population standard deviation

n represent the sample size  

ME = 4 the margin of error desired

Solution to the problem

When we create a confidence interval for the mean the margin of error is given by this formula:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}    (a)

And on this case we have that ME =4 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

n=(\frac{z_{\alpha/2} \sigma}{ME})^2   (b)

The critical value for 96% of confidence interval now can be founded using the normal distribution. The significance is \alpha=1-0.96 =0.04. And in excel we can use this formula to find it:"=-NORM.INV(0.02;0;1)", and we got z_{\alpha/2}=2.054, replacing into formula (b) we got:

n=(\frac{2.054(12)}{4})^2 =37.97 \approx 38

So then the minimum sample to ensure the condition given is n= 38

5 0
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Sindrei [870]

Answer:

x=12

Step-by-step explanation:

plug in 12 to x and results will make sense

7 0
3 years ago
/ (PPSP, 6.4B)
yanalaym [24]
It would be 1,602. Because if he pays 178$ every 4 months, you would divide 178 by 4 which is 44.50 then times it by 36 months which is 3yeara which gives you a total of 1602$
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