# Thread: Head & Tail problem

1. ## Head & Tail problem

Say, I have unfair coin. When I toss it, probability of a head is 0.1, and probability of a tail is 0.9.

I toss this coin 10 times. What is the probability I get 7 heads and 3 tails?

I tried to draw a tree, but after 10 levels I gonna have 1024 branchs. My calculator has Pr and Cr functions, but I don't even know it's a Pr or Cr problem.

Sorry I'm not a good math people.

2. You can solve this very easily if you know what the Bernoulli law is.
You have two opposite results:
Let's call the probability to get head: p = 0.1
Let's call the probability to get tail: q = 0.9
Since 1-0.9=0.1 the results are opposite. (First condition to apply Bernoulli Law)

The number of times we toss the coin is called: n = 10
Each toss is independant from the previous one. (Second condition to apply Bernoulli Law)
Finally we call the number of times we get head: x
In that case:
$P(x=7) = C^{7}_{10} \cdot 0.1^7 \cdot 0.9^3 = 8.748 \cdot 10^{-6}$

3. cheers,
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