We will see that the probability of picking two orange marbles without replacement is 0.23
<h3>
How to get the probability?</h3>
If we assume that all the marbles have the same probability of being randomly picked, then the probability of getting an orange marble is given by the quotient between the number of orange marbles and the total number of marbles, this gives:
P = 6/12 = 1/2
And then we need to get another orange marble, without replacing the one we picked before, this time there are 5 orange marbles and 11 in total, so the probability is:
Q = 5/11
Finally, the joint probability (of these two events happening) is the product of the probabilities, so we get:
P*Q = (1/2)*(5/11) = 0.23
If you want to learn more about probability, you can read:
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The difference between causation and correlation is that, Causation is characterized by cause-and-effect while correlation establishes a probable relationship.
<h3>What is the difference between Causation and correlation?</h3>
While Causation is characterized by a situation in which an action certainly causes an outcome and hence, is described as a cause-and-effect relationship, Correlation on the other hand only establishes a relationship between the two events and doesn't necessarily ascertain the occurrence of the other event .
An example of two variables which may be correlated is; the height and weight of an individual in which case it is generally perceived that taller people are heavier.
Read more on correlation and causation;
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It should be noted that the mean and the standard deviation of the data given in will be 4.26 and 1.1011 respectively.
<h3>How to solve
the mean.</h3>
From the complete information, the mean will be calculated as:
= (0.02 × 1) + (0.09 × 2) + (0.12 × 3) + (0.15 × 4) + (0.62 × 5)
E(X) = 4.26
The standard deviation will be calculated thus:
E(X²) = (0.02 × 1²) + (0.09 × 2²) + (0.12 × 3²) + (0.15 × 4²) + (0.62 × 5²)
E(X²) = 19.36
The standard deviation will then be the difference between the square root of 19.36 and 4.26². This will be 1.1011.
The expected profit of the company will be:
= 0.75 × E(X)
= 0.75 × 4.26
= $3.20
The mean of the total number of binders purchased will be:
= 4.26 + 2.74 = 7
The standard deviation will be 1.6658.
Lastly, the total expected profit will be:
= 0.75E(X) + 1.45E(Y)
= 0.75(4.26) + 1.45(2.74)
= 3.195 + 3.973
= 71.68
Learn more about standard deviation on:
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Answer:
y = -3(x + 1)² + 9
Step-by-step explanation:
y = a(x - h)² + k, where (h, k) is the vertex
The vertex of the quadratic function is (-1, 9)
The only equation listed that has a vertex at (-1, 9) is:
y = -3(x + 1)² + 9
