One in a Million V. One in a Billion

Probability Level 2

If you had a fair coin, that is one that flips heads and tails evenly, and flipped it 20 times in a row, the odds that all twenty of those flips will be heads is about $1 \text{ in a } 1,000,000$ .

If you kept flipping and kept turning up heads, how much more flips of heads would you have to get to for the odds to be at least $1 \text{ in a } 1,000,000,000$ ?

Ten more flips, flipping 30 heads in a row has one in a billion odds Two more flips, flipping 22 heads in a row has one in a billion odds Five more flips, flipping 25 heads in a row has one in a billion odds Twenty more flips, flipping 40 heads in a row has one in a billion odds One more flip, flipping 21 heads in a row has one in a billion odds