What is the lateral surface area of the triangular prism???
2 answers:
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Answer:
a) 60% probability that he picks up a blue pen and recognizes it as blue.
b) 62.5% probability that he chooses a pen and thinks it is blue.
c) 96% probability that he actually chose a blue pen.
Step-by-step explanation:
The problem has the following probabilities:
75 of 100 pens are blue, so a 75% probability that a pen is blue.
25 0f 100 pens are green, so a 25% probability that a pen is green.
If a pen is blue, an 80% probability that he thinks it is a blue pen
If a pen is blue, a 20% probability that he thinks it is a green pen.
If a pen is green, a 90% probability that he thinks it is a green pen.
If a pen is green, a 10% probability that that he thinks it is a blue pen.
a) (3pts) What is the probability that he picks up a blue pen and recognizes it as blue?
75% probability he picks up a blue pen.
80% that he recognizes a blue pen as blue.
60% probability that he picks up a blue pen and recognizes it as blue.
b) (3 pts) What is the probability that he chooses a pen and thinks it is blue?
75% probability that he picks up a blue pen.
80% that he recognizes a blue pen as blue.
25% probability that he picks up a green pen
10% probability that he thinks a green pen is blue.
62.5% probability that he chooses a pen and thinks it is blue.
c) (4pts) Given that he thinks he chose a blue pen, what is the probability that he actually chose a blue pen?
62.5% probability that he thinks that he choose a blue pen.
60% probability that he chooses a blue pen and think that it is blue.
96% probability that he actually chose a blue pen.
To solve the problem we must know about isosceles right triangle and the Pythagorean Theorem.
<h2>Isosceles Triangle</h2>A triangle with two sides of equal length and the corresponding angles of equal measurement is known as Isosceles Triangle.
<h2>Right Triangle</h2>A tringle with a 90° angle is known as a right-angled triangle.
The length of one leg of the large right triangle in terms of x is x√2.
<h2>Explanation</h2>Given to us
- If the altitude of an isosceles right triangle has a length of x units,
As it is given to us that the triangle is a right angle triangle the two sides of the triangle will be equal to each other.
therefore, AB = BC
Also, given that the altitude of the triangle is equal to x. therefore,
AB = x
AB = BC = x,
<h3>What is the largest side of the right triangle?</h3>We know that in a right-angled triangle the longest side of the triangle is the hypotenuse, which is always opposite to the 90° angle.
<h3>In ΔABC,</h3>AC is the hypotenuse,
Using Pythagoras theorem,
AC² = AB² + BC²
thus, the value of hypotenuse is x√2.
Hence, the length of one leg of the large right triangle in terms of x is x√2.
Learn more about Hypotenuse:
