How much time for life is possible?

conditions for life as we know it [4+6bn], from big bang to evaporation of last black hole: 1/1000 of (billionth x9)% #wondersoftheuniverse
— Chris Street (@ChrisGStreet) March 24, 2013

Notes

1. Life of Universe from Big Bang to end of Black Hole Era is 10^100 years
2. Life as we know it formed on earth formed ~4 billon years ago and cannot last for more than another 6 billion years (when our sun becomes a red giant) = 10^10
3. 10^10/10^100 = ~1/100% x 1/1000 x 1000,000,000 x 9 = (10^86)-1

Maths is quite right. What was the mistake I made??

Sources:

• Wonders of the Universe, Brian Cox, Pub. Harper Collins, 2011, pg 222
• Wonders of the Universe, Brian Cox, DVD, 2011