# Probability sum on a biased coin.

Q. If a biased coin with P(getting a 'Head')=1/3 is to be tossed till a head appears for the first time, then find P(more than 3 tosses are required to get a 'Head' for the first time).

My approach: This sum seems like a binomial probability sum, but i'm totally stuck, & cannot format the sum binomially.

If i format it binomially p=1/3, (1-p)=2/3, n=no of tosses, but when i'm trying to fix 'x' i'm stuck, as i can take 'x'=no of heads, but how can no of heads determine that the 'Head' came at the first time(during tossing)?

Please Help

Thank you

• Hint: The probability more than $3$ tosses are required is the probability the first $3$ tosses are tails. – André Nicolas Jul 10 '15 at 21:06
• All you want is the probability of throwing TTT on the first three rows. No binomial symbols involved. – lulu Jul 10 '15 at 21:06

## 1 Answer

You have to see it the other way around. This probability is the opposite to have the three first tosses being tails.