Probabilities (with b***s, literaly)

Aranarth:

An urn contains 16 white b***s and 9 black b***s. 10 b***s are extracted from the urn, with replacement. What is the probability that less than 6 b***s are white?

I'm stuck Someone could please help me?

There will be a lot of working to get this answer.
Firstly it is a binomial probablity.
This is because

1) There are only 2 outcomes for each trial (white or not white)
2) the probabiliy of success for each trial always stays the same
3) the trials are indepentant of one another.

P(white)=16/25
P(not white)=9/25

Now you have to use binomial probability for each of these scenarios (and then add them all together to get the final answer)
P(0 white), P(1 white) ....... P(5 white)
Do you know how to do that? Can you work it out? If you want more help I want to see what you have tried first.
The more you can workout yourself, the better your learning will be.

Sorry in advance for my english, it's not perfect and I might make some grammar mistake
First, i forgot to mention that the result should be [0.270842].

You are d**n right I did the right reasoning, but I made ​​some calculation errors (shame on me, you do not study mathematics at night!)
To apologize i'll post the solved exercize so it's avaible to other users.

Since they are repeated tests, you will have to apply Bernoulli:
P=nCr(n.k)*p^k*(1-p)^(n-k)
where, in this case, n=25 b***s, p=16/25 (possibilities to pick a white ball) and k is the number of the white b***s i am supposed to pick.

There are two ways to solve this:
1) To add P(0), P(1), P(2), P(3), P(4), P(5)
2) P=1-P(6)-P(7)-P(8)-P(9)-P(10)

Let's pick the first one. We need to apply Bernoulli to every case (no white b***s picked, 1 white ball picked, 2 white ball picked etc.)
P(0)= nCr(10,0)*(16/25)^0*(1-16/25)^10 = 0.0000365615844006
P(1) = nCr(10,1)*(16/25)^1*(1-16/25)^9 = 0.0006499837226779
P(2) = nCr(10,2)*(16/25)^2*(1-16/25)^8 = 0.0051998697814229
P(3)= nCr(10,3)*(16/25)^3*(1-16/25)^7 = 0.0246512345193382
P(4)= nCr(10,4)*(16/25)^4*(1-16/25)^6 = 0.0766927296157188
P(5) = nCr(10,5)*(16/25)^5*(1-16/25)^5 = 0.1636111565135335

We need to keep in mind that the events are incompatibles (if i pick 1 ball, i con't pick2 at the same time) and unconditioned (if i pick a ball and i put it again in the urn, the ball number will always be the same). The probability that less than 6 b***s are white is obtained adding the calculated probabilities between them:
P= 0.0000365615844006+0.0006499837226779+0.0051998697814229+0.0246512345193382+0.0766927296157188+0.1636111565135335 = 0.2708415357370919 = 0.270842

And here you go thanks melody