Math Help - Binomial Distribution

1. Binomial Distribution

There are 15children in a class
1)what is the probability that i)0 ii)1 iii)2 iiii) at least 3 were born in january.

Thank you

2. Let $p$ be the probability of a child who were born in January; $q$ be the probability of a child who were NOT born in January.

It is easy to see that $p=\frac{1}{12}$ and $q=\frac{11}{12}$

According to the Binomial Distribution: $p(y)=\binom{n}{y}p^yq^{n-y}$

Here we have $n=15$, for (i), (ii) and (iii), you can let $y=0$, $y=1$ and $y=2$ respectively.
Note for (iv), you can find the probability by $p(y\ge 3)=1-p(y\le 2)$

Roy
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