what is the probability of guessing correctly at least six of the ten answer in a true false objective test

Question

In your probability solutions

(1-252/1024)÷2 = 772/2048 how ?

Please explain it.

Answer 1

P(>6) = P(6) + P(7) + P(8) + P(9) + P(10)

10C6(1/2)^10 + 10C7)(1/2)^10 + 10C8(1/2)^10 + 10C9(1/2)^10 + 10C10(1/2)^10

=(1/2)^10[1+10+ 45 + 120 + 210) = (1/1024)(386) = about 37.7%

37.7% chance of getting 6 or more

37.7% chance of getting 4 or less

1-2(.377) = 1-.754 = 24.6% chance of exactly 5 right

(1/2)^10[10C5] = (1/1024)(10!/5!5!) = 252/1024 = about 24.6%

nCr = n!/r!(n-r)!