Question

If you flip a coin 12 times, what is the probability of ending up with more heads than tails?

Answer 1

For a fair-sided coin, probability p=0.5 for either head or a tail.

Binomially we have (½+½)¹²=1.

We need the sum of the first 6 terms: (½)¹²+12(½)¹²+66(½)¹²+220(½)¹²+495(½)¹²+792(½)¹²=0.3872 approx.

This is the probability of 12+11+10+9+8+7 heads, that is, the probability of 0+1+2+3+4+5 tails.