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blagie [28]
2 years ago
10

An ordinary (falr) dle is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a d

le is rolled twice in succession
and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.
Compute the probability of each of the following events.
Event A: The sum is greater than 8.
Event B: The sum is divisible by 5.
Write your answers as fractions.
(a) P(X) =

(b) P(B) =
Mathematics
1 answer:
ddd [48]2 years ago
6 0

By finding the number of outcomes that meet each criteria, we will see that the probabilities are:

  • A) P = 0.25
  • B) P = 7/36 = 0.194

<h3>How to find the probability?</h3>

We know that the fair die has 6 outcomes, so if we roll it twice, there are a total of:

6*6 = 36 outcomes.

To find the probability of getting a given event, we need to find the number of outcomes that make the event true.

A) The sum is greater than 8.

The outcomes that make this true are:

first roll    second roll     sum

 4                   5                 9

 4                   6                 10

5                     5                10

5                    6                 11

6                     3                 9

6                    4                 10

6                     5                11

6                     6                  12

3                     6                   9

So there are 9 outcomes whose sum is greater than 8, so the probability to getting this event is:

P = 9/36 = 0.25

B) The sum is divisible by 5.

The sum must be 5 or 10, the outcomes that give that are:

first roll    second roll     sum

   1                   4                 5

   2                  3                 5

   3                  2                 5

   1                   4                 5

   4                   6                10

  5                    5                10

   6                   4                 10

There are 7 outcomes, so the probability is:

P = 7/36 = 0.194

If you want to learn more about probability, you can read:

brainly.com/question/251701

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Answer:

Step-by-step explanation:

1) Mark two points on the line in the graph.

2) Determine the rise and run. Rise ---> difference in y-coordinates. (y2-y1)

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3) Plugin the values in the below mentioned formula.

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3 years ago
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7 0
2 years ago
PLEASEEE HURRYYY
Masteriza [31]

Answer:

(2,-5) and (2,1).

Step-by-step explanation:

We need to find the find all the points having an x coordinate of 2 whose distance from the point (-2,-4) is 5.

A circle with center (-2,-4) and radius 5 represents all the points whose distance from the point (-2,-4) is 5.

Standard form of a circle is

(x-h)^2+(y-k)^2=r^2

where, (h,k) is center and r is the radius.

(x-(-2))^2+(y-(-4))^2=(5)^2

(x+2)^2+(y+2)^2=25

Now, put x=2.

(2+2)^2+(y+2)^2=25

(4)^2+(y+2)^2=25

(y+2)^2=25-16

(y+2)^2=9

Taking square root on both sides.

y+2=\pm\sqrt{9}

y+2=\pm3

y+2=-3\text{ or }y+2=3

y=-5\text{ or }y=1

So, the y-coordinates of the points are -5 and 1.

Therefore, the required points are (2,-5) and (2,1).

8 0
3 years ago
Your state is considering raising the legal age for consumption of alcoholic beverages to 21 years old. How large a sample size
julsineya [31]

Answer:

n=\frac{0.5(1-0.5)}{(\frac{0.01}{2.58})^2}=16641  

And rounded up we have that n=16641

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by \alpha=1-0.99=0.01 and \alpha/2 =0.005. And the critical value would be given by:

z_{\alpha/2}=-2.58, t_{1-\alpha/2}=2.58

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

And on this case we have that ME =\pm 0.01 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

For this case we can use as estimator for the proportion \hat p =0.5, since we don't have any other previous info. And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.01}{2.58})^2}=16641  

And rounded up we have that n=16641

8 0
3 years ago
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solong [7]

Answer:

6

Step-by-step explanation:

8 0
3 years ago
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