Answer:
The probability that the good exam belongs to student <em>X</em> is 0.8571.
Step-by-step explanation:
It is provided that the probability that <em>X</em> did well in the exam is, P (X) = 0.90 and the probability that <em>X</em> did well in the exam is, P (Y) = 0.40,
Compute the probability that exactly one student does well in the exam as follows:
![P(Either\ X\ or\ Y\ did\ well)=P(X\cap Y^{c})+P(X^{c}\cap Y)\\=P(X)P(Y^{c})+P(X^{c})P(Y)\\=P(X)[1-P(Y)]+[1-P(X)]P(Y)\\=(0.80\times0.60)+(0.20\times0.40)\\=0.56](https://tex.z-dn.net/?f=P%28Either%5C%20X%5C%20or%5C%20Y%5C%20did%5C%20well%29%3DP%28X%5Ccap%20Y%5E%7Bc%7D%29%2BP%28X%5E%7Bc%7D%5Ccap%20Y%29%5C%5C%3DP%28X%29P%28Y%5E%7Bc%7D%29%2BP%28X%5E%7Bc%7D%29P%28Y%29%5C%5C%3DP%28X%29%5B1-P%28Y%29%5D%2B%5B1-P%28X%29%5DP%28Y%29%5C%5C%3D%280.80%5Ctimes0.60%29%2B%280.20%5Ctimes0.40%29%5C%5C%3D0.56)
Then the probability that <em>X</em> is the one who did well in the exam is:
![P(X\ did\ well\ in\ the\ exam)=\frac{P(X\cap Y^{c})}{P(X\cap Y^{c})+P(X^{c}\cap Y)}\\ =\frac{P(X)[1-P(Y)]}{P(X\cap Y^{c})+P(X^{c}\cap Y)} \\=\frac{0.80\times0.60}{0.56}\\=0.857143\\\approx0.8571](https://tex.z-dn.net/?f=P%28X%5C%20did%5C%20well%5C%20in%5C%20the%5C%20exam%29%3D%5Cfrac%7BP%28X%5Ccap%20Y%5E%7Bc%7D%29%7D%7BP%28X%5Ccap%20Y%5E%7Bc%7D%29%2BP%28X%5E%7Bc%7D%5Ccap%20Y%29%7D%5C%5C%20%3D%5Cfrac%7BP%28X%29%5B1-P%28Y%29%5D%7D%7BP%28X%5Ccap%20Y%5E%7Bc%7D%29%2BP%28X%5E%7Bc%7D%5Ccap%20Y%29%7D%20%5C%5C%3D%5Cfrac%7B0.80%5Ctimes0.60%7D%7B0.56%7D%5C%5C%3D0.857143%5C%5C%5Capprox0.8571)
Thus, the probability that the good exam belongs to student <em>X</em> is 0.8571.
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Answer:
Hope it helps
Step-by-step explanation:
Electricians usually charge between $50 to $100 per hour. For the entire project, you'll spend an average of $323, or within a range between $160 and $508 or more. Both hourly and project rates vary depending on the type of project, license and experience of the service provider.
Answer:
The red square, the green rectangle, the pink rhombus, and the green trapezoid.
Step-by-step explanation:
A quadrilateral is a shape that has 4 sides so all you have to do is count how many sides the shape has.
In mathematics, a polynomial is an algebraic expression containing more than two terms. When the polynomial could not be reduced to a lower degree, it is classified as a prime polynomial. Just like whole numbers, a prime polynomial cannot be broken down into factors except 1 and by the number itself. Take for example, the polynomial x² + 5x + 6. It can be reduces to its factors x=-2 and -3. That would be expressed to x² + 5x + 6 = (x+2)(x+3). But if the polynomial is, say, x² + 5x + 7, there is no roots that are whole numbers. Therefore, it can't be reduced into factored groups because it is a prime polynomial.
