Question

Apply the binomial theorem to 210 = (1 + 1)^10 . Answer each question in the work area provided below.

Answer 1

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 2

Answer:

Step-by-step explanation:

1) $(1+1)^{10} =\Sigma 10Cr (1)^r (1)^{10-r} \\=\Sigma 10Cr$

2) $1+10+45+120+210+252+210+120+45+10+1$

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 =$\frac{252}{2^{10} } \\=0.2461$

5) Getting 5 heads would be

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