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timurjin [86]
3 years ago
10

A 1010​-sided die is rolled. the​ die's faces are labeled with the numbers 1 through 1010​, and each number is equally likely to

be rolled. find the probability of rolling an eveneven number. what is the probability of rolling an eveneven ​number?
Mathematics
1 answer:
alina1380 [7]3 years ago
8 0
It sounds like the problem should read: "A 10-sided die is rolled. The die's faces are labeled with the numbers 1 through 10, and each number is equally likely to be rolled. Find the probability of rolling an even number. What is the probability of rolling an even number?"

If that is the case, then the answer as a fraction is 1/2 which is 0.5 in decimal form

How did I get this answer? There are 10 values (1, 2, 3, 4, 5, 6, 7, 8, 9, 10). Of that list, five values are even (2, 4, 6, 8, 10). Divide the two values
5/10 = 1/2 = 0.5
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Answer:

See below

Step-by-step explanation:

Permutation is to select an object then arrange it and it cares about the orders while Combination is about only selecting an object without caring the orders.

Permutation can be expressed in math as:

\displaystyle{_n P _r = \dfrac{n!}{(n-r)!} \ \ \ (n \geq r) }

where n is a number of total object and r is a number of selected object to arrange. Hence. n cannot be less than r.

Now let's see an example of permutation, suppose we have letter A, B and C. I'd like to know how many ways these words can be arranged:

Since there are 3 letters total and 3 selected letters to arrange then:

\displaystyle{_3 P _3 = \dfrac{3!}{(3-3)!}}\\\\\displaystyle{_3 P _3 = \dfrac{3 \times 2 \times 1}{0!}}\\\\\displaystyle{_3 P _3 = \dfrac{6}{1}}\\\\\displaystyle{_3 P _3 = 6}

Therefore, there are 6 ways to arrange the letters - we can also demonstrate visually:

ABC - 1

ACB - 2

BAC - 3

BCA - 4

CAB - 5

CBA - 6

Notice that if you do visually, you'll get the same answer as the calculation of permutation!

----

Combination can be expressed mathematically as:

\displaystyle{_n C _r = \dfrac{n!}{(n-r)!r!} = \dfrac{_n P _r}{r!} \ \ \ (n \geq r) }

The difference between permutation and combination is that you only find how many ways you can select object in combination. Therefore, no arrange and doesn't care about order, just ways to select.

Suppose we have same 3 letters: A, B and C. I want to find how many ways I can select these 3 letters:

Since there are 3 letters total and 3 selected letters:

\displaystyle{_3 C _3 = \dfrac{3!}{(3-3)!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{0!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{3!}}\\\\\displaystyle{_3 C _3 = 1}

Hence, there is only one way to select 3 letters. This makes sense because if you have 3 letters then you can only select 3 letters only one way.

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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