# What is the probability of a biased coin flipping heads (probability of heads is $\frac 35$) exactly $65$ times in $100$ trials?

A biased coin flips head with a probability $\frac 35$ and tails with probability $\frac 25$. The coin is flipped $100$ times. What is the probability that heads is flipped exactly $6$5 times?

I used binomial distribution for this

$$\binom nk\times p^k\times (1−p)^{n−k }$$

Which in this case gives:

$$\binom {100}{65}\times \left(\frac 35\right)^k\times \left(1-\frac 35\right)^{n−k }\sim 0.049133$$

Was my method and answer correct?

• Your method is okay. I have no calculator at hand. – drhab May 16 '16 at 12:48
• Both method and result are good. – lulu May 16 '16 at 12:50