A fair 2 sided coin is flipped 6 times. What is the probability that tails will be the result at least twice, but not more than 5 times?  Pick.
A) 5 / 8 B) 3 / 4 C) 7 / 8 D) 57 / 64 E) 15 / 16

Rationale: it would be easier to calculate the probability of opposite event and subtract it from 1 . opposite event : 0 tail , 1 tail , 6 tails . probability of getting no tails : 1 / 2 ^ 6 = 1 / 64 probability of getting 1 tail : 6 c 1 ∗ 1 / 2 ^ 6 = 6 / 64 , we must multiply by 6 c 1 or by 6 as tail can occur for any flip from 6 , hence in 6 ways ; probability of getting 6 tails : 1 / 2 ^ 6 = 1 / 6 ^ 4 p = 1 − ( 1 / 64 + 6 / 64 + 1 / 64 ) = 56 / 64 = 7 / 8 answer : c .
Answer: C