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zaharov [31]
3 years ago
6

A special roulette wheel, which has an equal number of red and black spots, has come up red four times in a row. Assuming that t

he roulette wheel is fair, what concept allows a player to know that the probability the next spin of the wheel will come up black is 0.5?
Concept of independent events
Concept of mutually exclusive events
Concept of dependent events
Concept of mutually inclusive events
Mathematics
1 answer:
Anna35 [415]3 years ago
3 0

Answer:

Concept of independent events

Step-by-step explanation:

Given that a special roulette wheel, which has an equal number of red and black spots, has come up red four times in a row.

We can assume that the roulette wheel is fair

We find that each time the result of a spin is independent of all the previous ones.

In other words, each spin result will not be affected by how many red or other got in the previous spins.

Mutually exclusive events are disjoint events so not right here.  Dependent is wrong because here independent.

So the concept here is

Concept of independent events

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A doctor released the results of clinical trials for a vaccine to prevent a particular disease. In these clinical​ trials, 200,0
CaHeK987 [17]

Answer:

1) No, there is  not  enough evidence to support the claim that the vaccine was effective (P-value=0.104) .

The null and alternative hypothesis are:

H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0

being the subindex 1 for the experimental group and subindex 2 for the control group.

2) Test statistic z=-1.26

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the vaccine was effective.

Then, the null and alternative hypothesis are:

H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0

The significance level is 0.01.

The sample 1 (experimental group), of size n1=100000 has a proportion of p1=0.0002.

p_1=X_1/n_1=21/100000=0.0002

The sample 2 (control group), of size n2=100000 has a proportion of p2=0.0003.

p_2=X_2/n_2=30/100000=0.0003

The difference between proportions is (p1-p2)=-0.0001.

p_d=p_1-p_2=0.0002-0.0003=-0.0001

The pooled proportion, needed to calculate the standard error, is:

p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{21+30}{100000+100000}=\dfrac{51}{200000}=0.00026

The estimated standard error of the difference between means is computed using the formula:

s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.00026*0.99974}{100000}+\dfrac{0.00026*0.99974}{100000}}\\\\\\s_{p1-p2}=\sqrt{0+0.0000000025}=\sqrt{0.0000000051}=0.000071

Then, we can calculate the z-statistic as:

z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.00009-0}{0.000071}=\dfrac{-0.00009}{0.000071}=-1.26

This test is a left-tailed test, so the P-value for this test is calculated as (using a z-table):

P-value=P(z

As the P-value (0.104) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

There is  not  enough evidence to support the claim that the vaccine was effective.

6 0
3 years ago
Point D is in the interior of ∠ABC. What is m∠DBC?
Rudiy27

37.5 degrees

we know angled like this always have 180 degrees total between the 2. which means we can set up a little equation to solve for x. The equation is (3x+22)+(x-4)= 180. Initially we can take the solid numbers (22 and -4) and get rid of them by taking them to the 180. 180- 22 is 158. 158 + 4 is 162. now we have 3x + x = 162. we combine like terms. means we end up with 4x =162. We now divide by 4 which means we get 40.5. Now we know x is 40.5. Now dbc is just 40.5- 4 which is 37.5.

3 0
2 years ago
What is the height h of the parallelogram
maxonik [38]
Area = base * height
Height = area / base

Height = base sin x
Where x = angle between side and the base
6 0
3 years ago
Expand 2x (5x-2) please help i’m confused
Leno4ka [110]
10x^2-4x is your answer! :)
8 0
3 years ago
<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B1.107%7D%7B123%7D%20%20%5Ctimes%20%20%5Cfrac%7B1.998%7D%7B333%7D%20%20%3D%20" id=
pav-90 [236]

Answer:

<h2>45 </h2>

Step-by-step explanation:

\frac{1.107}{123} \times \frac{1.998}{333} =

=   > 9 \times 6

= 45

6 0
3 years ago
Read 2 more answers
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