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Nitella [24]
2 years ago
13

On a multiple-choice test, each question has 4 possible answers. A student does not know

Mathematics
1 answer:
Mnenie [13.5K]2 years ago
6 0

Answer:

1.56% probability that the student gets all three questions right

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the student guesses the answer correctly, or he does not. The probability of the student guessing the answer of a question correctly is independent of other questions. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

Each question has 4 possible answers, one of which is correct.

So p = \frac{1}[4} = 0.25

Three questions.

This means that n = 3

What is the probability that the student gets all three questions right?

This is P(X = 3)

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 3) = C_{3,3}.(0.25)^{3}.(0.75)^{0} = 0.0156

1.56% probability that the student gets all three questions right

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A Quick Guide to the 30-60-90 Degree Triangle

The 30-60-90 degree triangle is in the shape of half an equilateral triangle, cut straight down the middle along its altitude. It has angles of 30°, 60°, and 90°. In any 30-60-90 triangle, you see the following: The shortest leg is across from the 30-degree angle, the length of the hypotenuse is always double the length of the shortest leg, you can find the long leg by multiplying the short leg by the square root of 3.

Note: The hypotenuse is the longest side in a right triangle, which is different from the long leg. The long leg is the leg opposite the 60-degree angle.

Two of the most common right triangles are 30-60-90 and the 45-45-90 degree triangles. All 30-60-90 triangles, have sides with the same basic ratio. If you look at the 30–60–90-degree triangle in radians, it translates to the following:

30, 60, and 90 degrees expressed in radians.

The figure illustrates the ratio of the sides for the 30-60-90-degree triangle.

A 30-60-90-degree right triangle.

A 30-60-90-degree right triangle.

If you know one side of a 30-60-90 triangle, you can find the other two by using shortcuts. Here are the three situations you come across when doing these calculations:

Type 1: You know the short leg (the side across from the 30-degree angle). Double its length to find the hypotenuse. You can multiply the short side by the square root of 3 to find the long leg.

Type 2: You know the hypotenuse. Divide the hypotenuse by 2 to find the short side. Multiply this answer by the square root of 3 to find the long leg.

Type 3: You know the long leg (the side across from the 60-degree angle). Divide this side by the square root of 3 to find the short side. Double that figure to find the hypotenuse.

Finding the other sides of a 30-60-90 triangle when you know the hypotenuse.

Finding the other sides of a 30-60-90 triangle when you know the hypotenuse.

In the triangle TRI in this figure, the hypotenuse is 14 inches long; how long are the other sides?

Because you have the hypotenuse TR = 14, you can divide by 2 to get the short side: RI = 7. Now you multiply this length by the square root of 3 to get the long side:

The long side of a 30-60-90-degree triangle.

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3 years ago
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