Find the theoretical probability simplify completely, №11409686, 16.09.2020 01:09

Mathematics

Find the theoretical probability. Simplify completely.

Step-by-step answer

P Answered by PhD

2

1/2

Explanation:

There are 8 number in the set

And 4 of them are even

We can write it
P(even) = 4/8 = 1/2

Mathematics

Find the theoretical probability. Simplify completely.

Step-by-step answer

P Answered by PhD

3

3/8

Step-by-step explanation:

Favorable outcome is 3

Total outcome is 8

P(1, 2, or 3) = $\frac{3}{8}$

Mathematics

Apply the binomial theorem to 210 = (1 + 1)10 . Answer each question in the work area provided below. 1. Write out the equation using combination notation. 2. Simplify each term. Do not combine the terms. 3. In two or more complete sentences, describe the relationship between the terms of the equation and the number of combinations when flipping a coin 10 times. 4. What is the theoretical probability of getting exactly 5 heads in a sequence of 10 flips? 5. In two or more complete sentences, compare the theoretical probability of getting exactly

Step-by-step answer

P Answered by PhD

2

The following are the answer to this question:

Step-by-step explanation:

Binomial theorem Expression:

$\bold{(x+y)^n= {^n}C_0x^ny^0+{^n}C_1x^{n-1}y^1+{^n}C_2x^{n-2}y^2+...+{^n}C_{\gamma}x^{n-\gamma}y^\gamma}+...+ {^n}C_nx^0y^n$ Solution:

1)

$\to 2^{10} = (1 + 1)^{10}$

$= (1+1)^{10}= {^{10}}C_0\times 1^{10}\times 1^0+{^{10}}C_1\times 1^{9}\times 1^1+{^{10}}C_2\times 1^{8}\times 1^2+ \\ {^{10}}C_3 \times 1^{7}\times 1^3+{^{10}}C_4 \times 1^{6}\times 1^4+ {^{10}}C_5\times 1^{5}\times 1^5 \\+ {^{10}}C_6 \times 1^{4}\times 1^6+....+{^{10}}C_{10}\times 1^{0}\times 1^{10}$

$= {^{10}}C_0. 1^{10}. 1^0+{^{10}}C_1.1^{9}. 1^1+{^{10}}C_2.1^{8}.1^2+\\{^{10}}C_3.1^{7}.1^3+{^{10}}C_4. 1^{6}. 1^4+ {^{10}}C_5.1^{5}. 1^5 + {^{10}}C_6 . 1^{4}. 1^6+ \\ {^{10}}C_7 . 1^{3}. 1^7 + {^{10}}C_8 . 1^{2}. 1^8+ {^{10}}C_9 . 1^{1}. 1^9+{^{10}}C_{10}. 1^{0}. 1^{10}\\$

2)

Simplify:

$(1+1)^{10}=$

${^{10}}C_0. 1^{10}. 1^0+{^{10}}C_1.1^{9}. 1^1+{^{10}}C_2.1^{8}.1^2+\\{^{10}}C_3.1^{7}.1^3+{^{10}}C_4. 1^{6}. 1^4+ {^{10}}C_5.1^{5}. 1^5 + {^{10}}C_6 . 1^{4}. 1^6+ \\ {^{10}}C_7 . 1^{3}. 1^7 + {^{10}}C_8 . 1^{2}. 1^8+ {^{10}}C_9 . 1^{1}. 1^9+{^{10}}C_{10}. 1^{0}. 1^{10}\\$

$=1+10+45+120+210+252+210+120+45+10+1\\\\=1024$

3)

The $r^{th}$ word is the number of variations where a coin is redirected 10 times.

4)

Get the frequency of exactly five heads is: ${^{10}}C_{5}$ = 252

$=\frac{252}{1024}\\\\=\frac{126}{512}\\\\=\frac{63}{256}\\\\=0.24$

5)

To Get 5 heads will be:

$={^{10}}C_{5} \times (\frac{1}{2})^{10}\\\\=\frac{{^{10}}C_{5}}{2^{10}}\\\\=0.24$

Mathematics

Apply the binomial theorem to 210 = (1 + 1)^10 . answer each question in the work area provided below. 1. write out the equation using combination notation. 2. simplify each term. do not combine the terms. 3. in two or more complete sentences, describe the relationship between the terms of the equation and the number of combinations when flipping a coin 10 times. 4. what is the theoretical probability of getting exactly 5 heads in a sequence of 10 flips? 5. in two or more complete sentences, compare the theoretical probability of getting exactly

Step-by-step answer

P Answered by Specialist

24

Use ^ to indicate an exponent. x^10 = x¹⁰

The coefficients of the expansion of (1+1)¹⁰ are: 1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1

(1+1)¹⁰ = 1·1¹⁰·1⁰ + 10·1⁹·1¹ + 45·1⁸·1² + + 10·1¹·1⁹ + 1·1⁰·1¹⁰
= 1 + 10 + 45 + 120 + 210 + 252 + 210 + 120 + 45 + 10 + 1

Thank you for posting your question here at . I hope the answer will help you. Feel free to ask more questions.

Mathematics

Apply the binomial theorem to 210 = (1 + 1)10 . Answer each question in the work area provided below. 1. Write out the equation using combination notation. 2. Simplify each term. Do not combine the terms. 3. In two or more complete sentences, describe the relationship between the terms of the equation and the number of combinations when flipping a coin 10 times. 4. What is the theoretical probability of getting exactly 5 heads in a sequence of 10 flips? 5. In two or more complete sentences, compare the theoretical probability of getting exactly

Step-by-step answer

P Answered by PhD

2

The following are the answer to this question:

Step-by-step explanation:

Binomial theorem Expression:

$\bold{(x+y)^n= {^n}C_0x^ny^0+{^n}C_1x^{n-1}y^1+{^n}C_2x^{n-2}y^2+...+{^n}C_{\gamma}x^{n-\gamma}y^\gamma}+...+ {^n}C_nx^0y^n$ Solution:

1)

$\to 2^{10} = (1 + 1)^{10}$

$= (1+1)^{10}= {^{10}}C_0\times 1^{10}\times 1^0+{^{10}}C_1\times 1^{9}\times 1^1+{^{10}}C_2\times 1^{8}\times 1^2+ \\ {^{10}}C_3 \times 1^{7}\times 1^3+{^{10}}C_4 \times 1^{6}\times 1^4+ {^{10}}C_5\times 1^{5}\times 1^5 \\+ {^{10}}C_6 \times 1^{4}\times 1^6+....+{^{10}}C_{10}\times 1^{0}\times 1^{10}$

$= {^{10}}C_0. 1^{10}. 1^0+{^{10}}C_1.1^{9}. 1^1+{^{10}}C_2.1^{8}.1^2+\\{^{10}}C_3.1^{7}.1^3+{^{10}}C_4. 1^{6}. 1^4+ {^{10}}C_5.1^{5}. 1^5 + {^{10}}C_6 . 1^{4}. 1^6+ \\ {^{10}}C_7 . 1^{3}. 1^7 + {^{10}}C_8 . 1^{2}. 1^8+ {^{10}}C_9 . 1^{1}. 1^9+{^{10}}C_{10}. 1^{0}. 1^{10}\\$

2)

Simplify:

$(1+1)^{10}=$

${^{10}}C_0. 1^{10}. 1^0+{^{10}}C_1.1^{9}. 1^1+{^{10}}C_2.1^{8}.1^2+\\{^{10}}C_3.1^{7}.1^3+{^{10}}C_4. 1^{6}. 1^4+ {^{10}}C_5.1^{5}. 1^5 + {^{10}}C_6 . 1^{4}. 1^6+ \\ {^{10}}C_7 . 1^{3}. 1^7 + {^{10}}C_8 . 1^{2}. 1^8+ {^{10}}C_9 . 1^{1}. 1^9+{^{10}}C_{10}. 1^{0}. 1^{10}\\$

$=1+10+45+120+210+252+210+120+45+10+1\\\\=1024$

3)

The $r^{th}$ word is the number of variations where a coin is redirected 10 times.

4)

Get the frequency of exactly five heads is: ${^{10}}C_{5}$ = 252

$=\frac{252}{1024}\\\\=\frac{126}{512}\\\\=\frac{63}{256}\\\\=0.24$

5)

To Get 5 heads will be:

$={^{10}}C_{5} \times (\frac{1}{2})^{10}\\\\=\frac{{^{10}}C_{5}}{2^{10}}\\\\=0.24$

Mathematics

Apply the binomial theorem to 210 = (1 + 1)^10 . answer each question in the work area provided below. 1. write out the equation using combination notation. 2. simplify each term. do not combine the terms. 3. in two or more complete sentences, describe the relationship between the terms of the equation and the number of combinations when flipping a coin 10 times. 4. what is the theoretical probability of getting exactly 5 heads in a sequence of 10 flips? 5. in two or more complete sentences, compare the theoretical probability of getting exactly

Step-by-step answer

P Answered by Specialist

24

Use ^ to indicate an exponent. x^10 = x¹⁰

The coefficients of the expansion of (1+1)¹⁰ are: 1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1

(1+1)¹⁰ = 1·1¹⁰·1⁰ + 10·1⁹·1¹ + 45·1⁸·1² + + 10·1¹·1⁹ + 1·1⁰·1¹⁰
= 1 + 10 + 45 + 120 + 210 + 252 + 210 + 120 + 45 + 10 + 1

Thank you for posting your question here at . I hope the answer will help you. Feel free to ask more questions.

Mathematics

You roll a number cube once. What is the theoretical probability that you roll a 2 or 4? Enter your answer as a simplified fraction.Use/to write your fraction. The probability that you roll a 2 or 4 is

Step-by-step answer

P Answered by PhD

3

Step-by-step explanation:

Probability of a 2 = 1/6

Probability of a 4 = 1/6

probability of a 2 or 4 = 1/6 + 1/6 = 2/6 = 1/3

Mathematics

You roll a number cube once. What is the theoretical probability that you roll a 5 or 2? Enter your answer as a simplified fraction. The probability that you roll a 5 or 2 is

Step-by-step answer

P Answered by PhD

1

The probability that you roll a 5 or 2 is $\frac{1}{3}$

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question:

There are 6 total outcomes(all numbers from 1 to 6).

The desired are 2, that is, rolling 2 or rolling 5.

p = 2/6 = 1/3

The probability that you roll a 5 or 2 is $\frac{1}{3}$

Mathematics

You roll a number cube once. What is the theoretical probability that you roll a 2 or 4? Enter your answer as a simplified fraction.Use/to write your fraction. The probability that you roll a 2 or 4 is

Step-by-step answer

P Answered by PhD

3

Step-by-step explanation:

Probability of a 2 = 1/6

Probability of a 4 = 1/6

probability of a 2 or 4 = 1/6 + 1/6 = 2/6 = 1/3

Mathematics

Nicole is rolling a dice for a probability project. What is the theoretical probability that she will roll a 1 or a 4? Write your answers as a simplified fraction OR a percent

Step-by-step answer

P Answered by PhD

$\frac{1}{3}$

Step-by-step explanation:

Given: Nicole is rolling a dice for a probability project

To find: theoretical probability that she will roll a 1 or a 4

Solution:

Theoretical probability expresses the chances that something will occur. It is equal to the number of favorable outcomes divided by the total number of outcomes.

Total number of outcomes = 6

Theoretical probability that she will roll a 1 or a 4 = $\frac{1}{6} +\frac{1}{6} =\frac{2}{6}=\frac{1}{3}$

Find the theoretical probability simplify completely P(4)

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