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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 5 heads with the fraction in your histogram. Interpret any differences.

Respuesta :

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

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Answer:

Step-by-step explanation:

1) [tex](1+1)^{10} =\Sigma 10Cr (1)^r (1)^{10-r} \\=\Sigma 10Cr[/tex]

2) [tex]1+10+45+120+210+252+210+120+45+10+1[/tex]

3) The rth term is the number of combinations of getting r heads when a coin is flipped 10 times

4) Getting exactly 5 heads frequency = 10C5 =252

Prob =[tex]\frac{252}{2^{10} } \\=0.2461[/tex]

5) Getting 5 heads would be

10C5 (1/2)^10 =0.2461 same as above.

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