# Solving question by binomial probability. If, over a given period in Brisbane, rain falls at random on 4 days of every 10, find the probability that the first 2 days of a given week will be wet and the remainder of the week fine.

Solving question by binomial probability
If, over a given period in Brisbane, rain falls at random on 4 days of every 10, find the probability that the first 2 days of a given week will be wet and the remainder of the week fine.
using the formula $\left(nCx\right)\left({p}^{x}\right)\left(\left({p}^{\prime }{\right)}^{n-x}\right)$
I put $n=10,x=2,p=0.4,{p}^{\prime }=0.6$
and I got 0.12, but the actual answer is 0.012.
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Sugainkohr
Step 1
You do not need to use the formula for the binomial distribution. Just calculate the first two days are rainy and the following 5 days are fine:
${p}^{2}\cdot \left(1-p{\right)}^{5}$
Step 2
The days, which are rainy and the days which are fine, are fixed.